Papers

The exact distribution of the sample variance for $n=3$ is known since Rietz (1931) for the uniform parent, and Royen (2007, 2008) gave a Fourier series for any bounded continuous parent. Neither settles which parents admit a finite closed form, nor which special functions it forces. In coordinates aligned with the cube diagonal the variance constraint becomes a cylinder and the cube cross-section a polygon with $S_3$ symmetry, hexagonal over the central band of the diagonal and triangular near either corner; the CDF is the volume of their intersection, the parent density entering as a weight. A closure hierarchy is then organized by the minimal function class containing the parent density: polynomial parents on any bounded interval always close in elementary terms, a theorem for the whole class; in the negative direction a single explicit parent already suffices, and for a rational one we prove the CDF is not elementary, the obstruction being an irreducible dilogarithmic part. Beyond those two theorems the hierarchy is a set of example-specific obstructions rather than a classification: for an algebraic parent the radial first-kind differential is shown non-elementary on a genus-two curve, and the exponential row is a conjecture supported by the Bessel structure of its radial integral. For the uniform parent we obtain a two-piece formula bifurcating at $Y=1/4$, where the variance disk first circumscribes the hexagonal cross-section at the cube center. For the singular arcsine parent we derive both endpoint laws in closed form and give a six-term approximation accurate to about $10^{-3}$, an accuracy Royen's universal series reaches at about a hundred terms.

Methods: We analyze TESS photometric data, radial velocity measurements, and eclipse timing variation curves for the triple star system, TIC 366240660, with a photodynamical code to infer the properties of all three stars and orbital motions. Results: With an outer orbital period of only 30.5 d, this is the second most compact triple reported in the literature. We have determined the masses and $T_{\rm eff}$ values of the three stars with an accuracy of about 1% and the radii to about 2%. The inclination angles of the two planes, and the mutual inclination angle are found with an accuracy of better than 1/3$^\circ$. The system is determined to be quite flat (to within 1/2$^\circ$), but with an outer eccentricity of $e_{\rm out} \simeq 0.33$. We find that the properties of the secondary star of the inner binary are completely inconsistent with the evolution of a single star in isolation, and it must have transferred most of its envelope to the current primary star in the inner binary during a prior episode of mass transfer. The eclipse timing variation (ETV) curve derived from the TESS photometric data shows that, in addition to a typical dynamical delay curve at the period of the outer orbit, there is also a much larger amplitude anomalous sinusoidal-like delay with a period of 840 d. This latter feature in the ETV curve is not yet describable in simple analytic terms, but it appears certain that it can be explained by the near integer ($\simeq$13:1) ratio of the outer to the inner orbital periods. Conclusions: We have extensively explored the exotic and anomalous ETVs of this highly compact triple system and found that they can exceed hours for the inner binary eclipses, and several days for the outer orbital eclipses. We provide a preliminary explanation for how these are related to the 13:1 mean motion resonance of the outer to inner orbits.

Low-light image enhancement (LLIE) is an im- portant component of visual sensing systems operating under degraded illumination, including nighttime surveillance, au- tonomous navigation, remote sensing, and inspection in poorly lit industrial environments. Most LLIE methods rely on output- level reconstruction losses that supervise only the final restored image, leaving the intermediate feature recovery process weakly constrained. This paper proposes MirrorDistill, an illumination- aware latent distillation framework that links the low-light and clean domains through feature mirroring. During training, a shared encoder and an exponential-moving-average teacher decoder process the clean reference image to generate clean- domain latent targets. These targets supervise the low-light student at two levels: raw encoder features and standardized multi-scale decoder projections. The alignment is applied layer by layer, while a proposed illumination-aware weighting scheme gives greater emphasis to underexposed regions. The teacher and reference branches are used only during training, so inference requires only the lightweight student encoder-decoder and in- troduces no teacher-side computational cost. Under evaluation on the standard LOL benchmarks, MirrorDistill outperforms the state-of-the-art methods on the real-captured LOL-v2-Real set, while having the lowest compute complexity (GMACs) and while remaining competitive on the LOL-v1 and LOL-v2-Synthetic datasets. Ablation studies further show the contributions of the encoder mirror, decoder mirror, and illumination-aware weighting. Finally, we release our code as open-source for the benefit of future research.

Padé resummation of the correlation energy from Møller-Plesset (MP) perturbation theory is not size-consistent and is therefore seldom used. We present an orbital-based Padé resummation of the MP2 and MP3 self-energy operators, whose trace yields a size-consistent correlation energy. We find that damping the third-order same-spin contribution leads to substantially increased accuracy, with the resulting same-spin damped orbital Padé resummed (SSD-OPMP3) approach attaining near-chemical accuracy (mean absolute error $\sim$ 1 kcal/mol) for total atomization energies of non-multireference molecules in the W4-17 dataset against the gold standard CCSD(T) method. Excellent performance surpassing CCSD is also obtained for other molecular datasets such as those containing barrier heights, noncovalent interactions, dipole moments, static polarizabilities, and transition-metal chemistry. SSD-OPMP3 is thus a highly accurate electronic structure method with the same noniterative $O(N^6)$ cost as MP3, filling a gap in the cost/accuracy hierarchy of wavefunction methods.

Reactive power is not uniquely defined for nonsinusoidal voltage and current waveforms because different scalar readouts can assign different values to the same measured voltage–current waveform pair. This paper characterizes which scalar readouts are selected by specific measurement and physical requirements, and quantifies the current information lost through scalarization. The scalar readout is first restricted by requiring bilinearity, alternation, and invariance to the measurement time origin. Requiring it to vanish for all smooth, strictly monotone, time-invariant memoryless resistors then forces the harmonic weights to be proportional to harmonic order. With consistency across harmonic cutoffs and fundamental-frequency calibration, this uniquely yields the classical derivative, or Iliovici-type, scalar within the stated class. The selected weighting is also incompatible with conventional reactive-power calibration independently at every harmonic. Furthermore, for known nonzero voltage, active power and a finite set of skew scalar readouts leave an affine family of compatible currents of exact dimension \(d-1-r_v\). These results establish explicit selection and information-loss limits for scalar reactive-power measurements under nonsinusoidal conditions.

We report the structural and optical properties of nanoscale Sr2IrO4 freestanding thin-films fabricated using a water-soluble Sr3Al2O6 layer. The coherent lattice structure, phonon modes, two-magnon Raman scattering, and optical absorption spectra of the Sr2IrO4 nanomembrane are analogous to those of the layered iridate epitaxial thin-films and single crystals. Remarkably, the formation of 3-unit-cell-thick SrIrO3 and interfacial composite layers alleviates antiphase boundaries at the Sr2IrO4/Sr3Al2O6 interface, resulting in structurally-robust nanomembranes. Our experimental results show that this freestanding thin-film approach of layered oxides can provide techniques for tuning or realizing unprecedented states beyond conventional thin-film methods, suggesting a pathway in achieving flexible layered-oxide electronics.

Purpose: Assessing grant applications is time-consuming and difficult, adding to the overall burden of academic peer review. Whilst funders are exploring whether AI can help, there is no published research into the accuracy of Large Language Models (LLMs) for scoring contemporary grants. Design/methodology/approach: This study investigates whether six open-weight LLMs (Gemma 3 1B/4B/12B/27B, DeepSeek R1 32B, Qwen 3 32B) can give useful scores for 2267 recent UK Economic and Social Research Council (ESRC), and Engineering and Physical Sciences Research Council (EPSRC) grant applications, comparing them with scores from the original reviewers and funding panel members. Findings: Although the LLM scores are individually inaccurate, when averaged and converted to ranks they correlate positively with expert average scores. The best performing LLM, Gemma 3 27B (10 iterations with varied prompts), had moderate rank correlations with average reviewer scores (mean rho=0.26). Gemma 3 27B's average correlation with individual reviewers was 0.19, which is lower than the inter-reviewer mean correlation of 0.24, suggesting that it scores are slightly weaker than individual reviewer scores. Gemma 3 27B had weak rank correlations with average panel member scores (mean rho=0.17), with lower average correlations with individual panellists (mean rho=0.14), which is substantially lower than the inter-panellist correlation (mean rho=0.38). Whilst the correlations seem too weak to replace expert review at the final panel stage, LLM scores might help with the initial reviewing state, such as by helping identify the weakest proposals for fast-track desk rejections, to replace one human reviewer, or for triangulation to check for bias.

Multivariate time series contain complex patterns that span across both space and time. While covariance-based statistical tools like spatiotemporal Principal Component Analysis (ST-PCA) help identify these patterns, they are limited to linear operations and prone to estimation errors with limited data. Recent covariance-based spatiotemporal neural networks offer more stable, non-linear alternatives, but they ignore correlations across different time steps. To solve this, we introduce the Kronecker coVariance Neural Network (KVNN), a temporal graph neural network that represents the spatiotemporal covariance matrix via a sum of Kronecker products where spatial and temporal dependencies are decoupled. By implementing filtering operations on spatial and temporal components, KVNNs achieve expressive processing capabilities, admit a rigorous spectral analysis, and are provably stable to finite-sample estimation errors, ultimately addressing all of ST-PCA's limitations. We show on five real-world datasets that KVNNs achieve strong forecasting performance, often requiring significantly fewer trainable parameters than competitive methods, and are consistent under estimation noise.

Large language models (LLMs) enable automated algorithm design (AAD) through reasoning and code synthesis. However, most existing LLM-based AAD methods separate algorithm design from target optimization, deploying a fixed design even as the optimization state evolves. Conventional adaptive optimizers can respond to such changes, but their adjustments remain confined to predefined parameters, operators, or strategies. To address these limitations, we introduce online LLM-based AAD, a novel optimization paradigm that treats the algorithm itself as a state-dependent decision variable. At each stage, LLM agents synthesize an algorithm with new behavior logic from the current optimization state. Executing the generated algorithm advances the search and provides feedback for subsequent designs, coupling algorithm design with target optimization without requiring a separate offline algorithm pretraining stage. To implement this paradigm, we propose OnDesign, a multi-agent framework that reconciles competing design perspectives to synthesize executable algorithms and uses execution feedback to refine how runtime evidence is interpreted for subsequent designs. We evaluate OnDesign across two mainstream black-box optimization paradigms on three scenarios: Bayesian optimization, evolutionary continuous optimization, and evolutionary mixed-variable optimization. Extensive experiments on six benchmark suites and one engineering problem across multiple problem dimensions demonstrate superior overall performance over conventional optimizers and offline LLM-based AAD methods.

We extend a Lagrangian formulation of dual electrodynamics by introducing electric and magnetic Higgs scalar fields. The scalars couple to Mandelstam nonlocal potentials which enter the electric and magnetic sectors. We consider the vacuum in which only the magnetic scalar has a nonzero expectation value. The generalised Maxwell equations remain local even though the scalar couplings are nonlocal. In this phase the local electric potential keeps a massless pole while the magnetic sector acquires a mass. The electric interaction is therefore Coulombian at large distances while the pole-pole and charge-pole interactions become short ranged. The magnetic charge is then screened in the sense of the Swieca theorem while the electric charge is not. The Dirac condition is inherited from the symmetric phase as a quantisation rule for the microscopic electric and magnetic couplings. We also comment on screened monopoles as possible dark sector degrees of freedom.

NASA's Astrophysics Division convened the Emerging Technologies for Astrophysics Missions (ETAM) Workshop in March 2025 at the Ames Research Center in Silicon Valley, California. The workshop's goal was to identify emerging technologies that could critically impact or enable future space missions-including concepts previously considered unachievable. Four key technology areas were examined: Astrophotonics, Artificial Intelligence and Machine Learning, Advanced Materials, and Quantum Sensors. Approximately 60 participants from academia, industry, government laboratories, and NASA centers attended. The workshop fostered an inspiring and collaborative atmosphere that encouraged interaction among experts both within and across disciplines. The workshop's three-day novel format featured landscape presentations outlining the state of each field, followed by breakout sessions where participants, grouped in their own disciplines, identified high-impact technologies for astrophysics missions. Cross-pollination sessions then brought together experts from multiple technology domains to foster interdisciplinary insights. The event successfully identified several high-priority emerging technologies (summarized in subsequent sections of this report). In addition to the field-specific insights, the workshop also produced five key cross-cutting suggestions for the NASA Astrophysics Division to consider.

Coordinated bimanual manipulation is challenging because the motion of either arm can alter the shared 3D scene and thereby affect the other arm. Yet most diffusion policies generate actions without explicitly modeling these future geometric consequences, while predictive variants typically use future state only as auxiliary supervision or fixed conditioning. We address this limitation by proposing JAMB, a diffusion policy that jointly denoises bimanual actions and future 3D point tracks. By allowing action and track hypotheses to evolve together within a shared Transformer, each can inform and refine the other throughout denoising. We further ground multimodal representations in a shared spatiotemporal coordinate system to facilitate geometry-aware interaction during joint denoising. We evaluate JAMB on diverse bimanual manipulation tasks in RoboTwin 2.0 and on a real-world robot, comparing it with action-only policies and alternative future-prediction approaches spanning different state representations and learning objectives. Across 16 simulation tasks, JAMB achieves an average success rate of 83.4%, outperforming the strongest baseline by 23.9 percentage points. On three real-world tasks, it outperforms the action-only and auxiliary geometry prediction methods by 50.0 and 21.2 percentage points, respectively. Beyond these performance gains, JAMB shows stronger generalization to cluttered scenes and out-of-distribution backgrounds than the evaluated baselines. Together, these results demonstrate the effectiveness of our joint action-motion modeling framework for coordinated bimanual manipulation. Our project website is available at https://jam-bimanual.github.io/

In this paper, we analyze square-mean Weyl almost periodic solutions and square-mean Weyl double-measure pseudo almost periodic solutions for a class of semilinear evolution equations in separable Hilbert spaces driven by two-sided fractional Brownian motion with Hurst index $H<1/2$. Due to the non-integrability of covariance density for $H<1/2$, a Hölder-continuity condition on the diffusion coefficient is required. An illustrative example involving a stochastic parabolic equation demonstrates the applicability of obtained results.

The shape of the correlation function of galaxy pairs can be used as a cosmological distance indicator. Most estimators of this shape require that one bin the pair counts, and considerable effort is expended in finding the optimal bin size. Cosmological constraints are then derived, in a separate step, by fitting to the binned pair counts. By projecting the pair counts on a suitable basis set, it is possible to estimate the pair correlation function without binning. Recent work suggests that, in the context of estimating the cosmological distance scale from galaxy clustering data, polynomials and half-integer generalized Laguerre functions are particularly useful bases. We show how to use these bases to measure the correlation function and estimate the reconstructed distance scale in a single step. Our analysis includes the effects of shot-noise and cosmic variance, and highlights the benefits of projecting pair counts onto orthogonal basis functions.

Ultra low-field MRI expands global access to neuroimaging but produces scans with low signal-to-noise ratio, reduced contrast, and thick slices. While regression-based super-resolution can recover anatomical detail for segmentation, it returns a single deterministic estimate that gives no indication of regions where the low-field input leaves anatomy underdetermined. Generative diffusion models offer an alternative by sampling the posterior distribution of plausible high-field images, quantifying this anatomical ambiguity. However, applying them to 3D whole-brain MRI is restricted by memory bottlenecks, slow sampling, and scanner domain shifts. We propose a 3D residual wavelet diffusion model that combines three ideas to overcome these hurdles. A lossless wavelet reparameterisation shrinks the spatial grid to fit a whole brain on a single GPU, residual shifting accelerates sampling by starting from the low-field input, and domain randomisation promotes scanner generalisation without paired training data. As the high-field reference is not a voxel-aligned ground truth, we evaluate downstream volumetric agreement. On a healthy cohort (n=19) imaged at 0.064T and 3T, our method matches a leading general-purpose regression approach in volumetric accuracy while additionally generating per-voxel uncertainty maps highlighting underdetermined regions. Furthermore, on a pilot dataset (n=11) of participants with cognitive impairment, disease-relevant atrophy is preserved rather than normalised towards a healthy prior. Our framework brings whole-brain posterior sampling to low-field super-resolution without sacrificing volumetric accuracy.

Direct collisions in the inner pc of the Galactic center can alter the orbits and properties of stars. The outcome of a collision depends on a number of parameters, including the masses and ages of the stars, the impact parameter, and the initial relative velocity. We utilize the newly developed $\verb|collAIder|$, a machine learning tool developed to predict the outcomes of stellar collisions, to bridge 3D hydrodynamic simulations of stellar collisions with a dynamical model of the Galactic center. Our results show a substantial population of stripped stars, $\sim$$10\%$ of the initial stellar population, produced by mass loss during high-speed collisions. Stellar mergers are less frequent, with about $5\%$ of the stars experiencing a collision-induced merger. We also find that high-speed, nearly head-on collisions can completely disrupt the stars. These destructive collisions are usually preceded by 10 or more collisions, which gradually reduce the mass of the star before it is ultimately destroyed. We estimate that mass loss during stellar collisions injects roughly $(2.5-8)\times 10^5$ M$_\odot$ of gas into the surrounding environment. Most of this gas is injected into the inner $0.1$ pc and about $90\%$ is retained within the cluster and may be accreted onto the supermassive black hole.

Barium zirconate titanate, Ba(Zr$_x$Ti$_{1-x}$)O$_3$ (BZT), is a leading lead-free candidate for high-performance electronic components due to its highly tunable ferroelectric-to-relaxor transition. In this study, we employ molecular dynamics simulations to investigate the effects of local chemical clustering on the structural and functional properties of BZT in both ferroelectric (x = 0.2) and relaxor (x = 0.4) regimes. Crucially, we demonstrate that Zr clustering induces a significant enhancement of local polarization across both compositions. Rather than a purely volume-driven effect, this enhancement is fundamentally governed by a spatial redistribution of local structural phases (rhombohedral, orthorhombic, and tetragonal); Zr segregation forms larger, continuous Ti-rich regions that expand highly polar rhombohedral domains and foster cooperative dipolar alignment. This cooperative coupling thermally stabilizes the local polar order, systematically elevating the Curie, maximum permittivity, and Burns temperatures. Focusing on the relaxor composition (x = 0.4), chemical segregation promotes the formation of resilient, swirling polar topological textures,categorized into vortices circulating around Zr-rich clusters and interstitial vortices localized within the Ti-rich matrix. These topological structures act as effective pinning barriers against polarization reversal, driving pronounced electrical hardening with elevated coercive fields. Ultimately, these findings establish a quantitative link between nanoscale compositional heterogeneity, polar domain topology, and macroscopic performance, providing a robust framework for engineering lead-free perovskites via local chemical order control.

We describe a polytopal realization of categorical $n$-associahedra. The normal fan of this polytopal realization is a modification of the authors' velocity fan and was found by OpenAI's Astra model.

Temporal rainfall distributions are widely used in design storm construction; however, many countries with limited sub-daily observations, such as Brazil, still rely on frameworks developed under different hydroclimatic conditions. This mismatch may introduce bias in hydrological design and water resources estimation. Here, we develop the first national-scale empirical Huff curves for Brazil using sub-daily rainfall observations. We compiled data from 3,164 stations and, after quality control, retained 290,164 storm events from 1,045 stations spanning 2010 to 2025. Empirical cumulative rainfall mass curves were constructed and fitted using seventh-degree polynomials at station, biome, state, and municipality scales. Our findings show a dominance of first-quartile (Q1; front-loaded) storm patterns, occurring at 94.4% of stations nationally, increasing to 99.2% in the Amazon and Cerrado biomes and decreasing to 88.7% in the Atlantic Forest. The national Q1 median curve closely matches the Huff (1967) reference (MAE = 0.045; Dmax = 0.097), with narrow bootstrap uncertainty. Q1 dominance is robust to inter-event time definition, with 84.7% of stations showing consistent classification across 2 to 12 h thresholds. A Soil Conservation Service Curve Number experiment across 579 headwater catchments shows that Brazilian curves increase design peak discharge by a median of 8% and up to 11% in the Cerrado relative to the Illinois reference, indicating potential underestimation when using non-local distributions. Biome-, state-, and municipality-scale parameters are provided as open data and through an interactive platform, offering locally calibrated design-storm alternatives for Brazil.

We establish an upper bound for the ground state energy density of a dilute Bose gas, interacting through a general short-range, repulsive potential. To reach this goal, we extend the approach recently introduced in [1] for hard spheres.

Motion correction in magnetic resonance fingerprinting (MRF) helps preserve the accuracy of quantitative maps; however, existing approaches provide motion updates only every 7-8 seconds. We propose a navigation framework that integrates compact k-space navigators throughout the MRF acquisition, enabling sub-second motion estimation at minimal sequence overhead. A 3D spiral-projection MRF sequence was augmented with three orthogonal spiral navigators inserted every 0.5 seconds, enabling motion estimation by comparing navigator signals with quantitative scout (Q-Scout) data, i.e., motion-free low-resolution k-space with matching contrast evolution. The Q-Scout is obtained via a rapid calibration during the dummy preparation period, incurring no additional scan time. Motion estimation is formulated as dictionary matching in a discriminant subspace with optimization refinement. The method was evaluated in simulation and in vivo for 1 mm isotropic brain 3D MRF at 3 T. Across 35 motion-corrupted acquisitions with motion-free references available, the proposed motion correction reduced MRF reconstruction normalized root-mean-square error (NRMSE) by 7.1% and increased the structural similarity index measure (SSIM) by 0.085. Motion estimates aligned with 8 second temporal-rate image-based navigation (mean absolute difference of 0.15 mm and 0.23 degrees), while the proposed method provided higher temporal resolution and improved motion correction. The proposed framework enables robust motion navigation in MRF at 0.5 second temporal resolution with minimal sequence overhead. By using contrast-consistent modeling and efficient inference, it improves the reliability of quantitative MRI under rapid, unpredictable motion.

Plasticity is invoked across the sciences to explain how systems can change, yet it is inferred from the very change it is meant to explain. A system may have many alternatives, realize none and still be plastic. Another may be driven far toward its only alternative, but the magnitude of that change does not establish its plasticity. What matters for plasticity is not how far the system moves but how strongly its present configuration constrains alternatives. Here I propose that plasticity, understood as a prospective property, is inverse configurational constraint: a system is plastic to the extent that its present configuration weakly constrains displacement toward alternatives within a declared representation. For systems sharing a functional partition, structural representation, and normalized architecture, increasing plasticity lowers every positive finite structural barrier separating the current state from its alternatives. With a fixed accessibility criterion, the accessible repertoire can expand but cannot shrink. In network representations, aggregate coupling is identified as configurational constraint, whose inverse defines plasticity. Barrier reduction and repertoire nesting are consequences, not components, of the definition. This connects two research traditions: quantifying connectivity without interpreting it as plasticity, and treating plasticity as a capacity for change without a prospective operational measure.

Emotion coping is inherently relational, unfolding through interactions with friends, family, professionals, and communities. Yet AI chatbots are largely designed around a user–AI dyad. Learning from the ethics of care, we examine how AI chatbots shape the relational conditions of emotion coping. We conducted a scenario-based study with 17 U.S. young adults across four emotion coping scenarios. Participants identified eight roles through which AI could support relational conditions, alongside three challenges: flattening distinct relational conditions, discouraging reciprocity, and shifting relational labor onto users. This study contributed a relational perspective of responsible AI in emotion coping. We argue that responsible AI should respond to individuals' situated relational conditions rather than provide general-purpose support. We further identify two design principles: fostering reciprocity by supplying materials to engage with others, and strengthening emotional self-efficacy. Together, we position responsible AI as AI in the loop of human relationships.

Topological signal processing (TSP) processes signals on simplicial complexes with oriented boundary operators, which is the natural choice for flow signals or when the topological invariants play a role for the task at hand. However, many higher-order signals carry no orientation, and applying oriented operators to them is not well-defined since it introduces an arbitrary choice of simplex orientation. We study an unoriented TSP (UTSP) framework that replaces oriented boundaries with unoriented incidence matrices. First, we show that unoriented incidence and Laplacian matrices between arbitrary simplicial levels admit graph-like spectral properties. Second, since dropping orientation removes the Hodge decomposition, we introduce an unoriented counterpart, termed interaction-order decomposition, which quantifies how much of a higher-order signal is explained by aggregating lower-order signals. Third, we use this decomposition to derive regularizers for signal reconstruction that penalize each interaction order separately. Experiments on real-world data show that the order-aware regularizers outperform oriented baselines, with the largest gains when the signal energy is unevenly distributed across orders.

In this paper, we study the deformed Hermitian-Yang-Mills (dHYM) equation on the non-compact Calabi-Yau manifold $Z = {\rm{Tot}}({\bf{K}}_{X})$, where $X$ is a rational homogeneous variety. Since $X$ is a Fano variety, $Z$ is a resolution of the singularity at the vertex of the affine cone ${\rm{Aff}}(X)$, provided the cone is built using the anticanonical polarization ${\bf{L}} = {\bf{K}}_{X}^{-1}$. Using the cohomogeneity-one symmetry of the Ricci-flat Kähler metric obtained via the Calabi ansatz on $Z$, we reduce the fully nonlinear PDE underlying the dHYM equation to a scalar, asymptotically autonomous ordinary differential equation (ODE). From this, we determine the exact condition on the topological phase that guarantees global existence of solutions. As an application, we show that every holomorphic line bundle over $Z$ admits a smooth, globally defined Hermitian connection solving the dHYM equation, provided the total phase lies in an explicit open interval determined by the Lie-theoretic data. Also, we prove a rigidity result classifying the exact geometric conditions under which the dHYM solution collapses into a classical Hermitian-Yang-Mills (HYM) connection. The results established generalize previous constructions and provide a substantial new class of examples. Furthermore, the approach presented allows one to study the behavior of the dHYM solutions through ODE methods. Using this approach, we construct the first explicit non-trivial example of a Hermitian-Einstein connection on a line bundle over a non-toric Calabi-Yau manifold which is not dHYM.

In the matrix method for linear perturbations of spherical stellar systems, the perturbed potential and density are expanded over a set of potential-density pairs. For radial perturbations, mass conservation makes the coefficient of $1/r$ in the perturbed potential vanish, so that the potential decays faster than $1/r$. Starting from the $\ell=0$ Hernquist–Ostriker family, we construct in closed form a set of potential-density pairs whose potentials decay as $r^{-p}$ with a prescribed $p\ge2$, the tail containing all subsequent integer powers. For $p=2$ each pair is individually massless, and the potential of the $n$-th pair is expressed through a single Jacobi polynomial. We derive the combination weights, the leading tail coefficients and the Gram matrix analytically; the Gram matrix is banded with half-width $p-1$ (tridiagonal at $p=2$). The $n$-th potential element has exactly $n-1$ nodes, spread from $r\sim n^{-2}$ to $r\sim n^{2}$, so that the set resolves both the centre and the far periphery. As a test, the expansion of the dilation-mode potential of the isochrone model converges exponentially and carries no parasitic mass at any truncation, in contrast to the standard set.

We study determinantal planar Coulomb gases with a smooth radial potential, a smooth radial perturbation, jump-type singularities (including the bulk, semi-hard, hard, and soft-edge regimes), and a hard wall region given by a centered disk, a disk complement, or an annulus. We obtain explicit asymptotic expansions of the partition functions up to and including the term of order $1$. Our results unify and generalize many of the earlier works.

Retrieving similar mobile applications (apps) is essential for researchers, developers, and end-users. Researchers use similarity detection to study app ecosystems and trends, developers for competitor analysis, and end-users for focused app recommendations. Existing approaches rely on embedding-based retrieval, which captures semantic similarity but fails to identify functionally similar apps. To our knowledge, no prior work has applied large language model (LLM)-based filtering to this task, due to the high computational cost of evaluating large numbers of app pairs. To address this gap, we propose ReFilter, a hybrid framework that first Retrieves semantically related candidate apps using embeddings and then applies LLM-based contextual Filtering to identify true functionally similar apps with higher precision. This design balances efficiency and accuracy, achieving an F1-score of 90% for retrieving similar apps. By improving the relevance of app alternatives, ReFilter enables more accurate app comparisons and supports improved ecosystem understanding, competitor analysis, and recommendations.

We investigate the proximity-induced spin-orbit coupling (SOC) in graphene on transition-metal dichalcogenide (TMD) heterostructures using a tight-binding approach. The tight-binding parameters of an effective 4-band model describing the low-energy physics of the graphene layer are extracted as a function of twist angle, material composition (MoS${}_2$, MoSe${}_2$, WS${}_2$, WSe${}_2$), band alignment, and charge-transfer dipole. We investigate the effect of a charge-transfer dipole induced on the chalcogen layer closest to graphene, which is typically neglected in tight-binding models but included in ab initio calculations through charge redistribution. In addition, we explore the influence of variations in the band alignment. We find that the spin-valley and Rashba spin-orbit coupling energies as well as the so-called Rashba phase, governing the orientation of momentum-space spin textures, show a strong dependence on the twist angle and electrostatic tuning. Our results suggest that variations in band alignment and charge redistribution contribute to the spread of spin-orbit parameters reported in the literature.

Teleoperation provides a critical safety fallback when autonomous vehicles (AVs) encounter scenarios that are outside their operational design domain. In practice, however, remote operators rely primarily on compressed camera streams over 5G, which often lack depth and spatial geometric cues for safe operation in complex dynamic environments. While multi-sensor fusion can enhance situational awareness, directly transmitting raw camera and LiDAR data is impractical due to 5G uplink bandwidth and latency constraints. In this paper, we propose SHARDED, a collaborative camera-LiDAR perception framework that deploys a feature-level fusion pipeline across the vehicle and edge to reduce uplink traffic while preserving 3D detection and depth estimation accuracy. We further design two complementary mechanisms for SHARDED: (i) A network-aware adaptive feature transmission mechanism that reduces data traffic by 50% on average (peaking at over 95%) compared to raw sensor data, and (ii) a latency-aware positional drift compensation mechanism to mitigate cross-modal misalignment induced by unstable network conditions. Evaluations on the nuScenes dataset and real-world 5G measurement traces show that SHARDED achieves competitive perception quality while reducing uplink bandwidth consumption and end-to-end latency.