Papers

JWST has uncovered an abundant population of compact, red sources at high redshifts, termed little red dots (LRDs). We study whether they could be explained by thermally relaxed, hydrogen-burning, metal-enriched supermassive stars (SMSs). We construct 1D models in hydrostatic and thermal equilibrium, including a radiation-pressure-dominated, CNO-burning core and an outer envelope with metallicity-dependent opacity, non-adiabatic convection, and an effective treatment of super-Eddington surface layers. The luminosity is close to the Thomson-scattering Eddington limit. The Fe-opacity bump drives the formation of a strongly inflated, low-mass envelope, while hydrogen recombination terminates the envelope at a bound photosphere. For M=$10^4$ to $10^6$ Msun and metal mass fractions $Z=10^{-4}$ to $10^{-2}$, we find that the most metal-rich models (Z ~ $10^{-2}$) develop highly inflated envelopes and reach Teff ~ 7000 K. We suggest that such enriched SMSs could instead be assembled through runaway stellar collisions in compact star clusters. The GR instability sets a maximum mass that depends on the core rotation rate. The nonrotating and rotating models have maximum masses $3\times10^5$ to $3\times 10^6$ Msun, and maximum luminosity of the order $10^{44}$ erg/s, comparable to the observed bright-end cutoff of the LRD luminosity function. Core hydrogen depletion can drive initially stable SMSs across the instability threshold after a lifetime of order 1 Myr. If each LRD leaves a black hole retaining most of its mass, the observed LRD abundance implies a present-day remnant density of order $10^{-2}\rm cMpc^{-3}$, consistent with the local abundance of supermassive black holes. Cool SMSs naturally produce weak X-ray and weak high-ionization lines. Non-LTE effects may significantly modify the Balmer features and the continuum opacity, and may lower Teff below our LTE value.

Vision Transformers devote most of their parameters to MLPs for channel mixing, but still rely on quadratic multi-head self-attention for token interactions. While linear attention fixes the complexity problem, bringing it down to O(N), it is usually just paired with the same fixed-activation MLP as before. Kolmogorov-Arnold Networks take a different approach, placing learnable univariate functions on the edges instead. However, existing vision KANs either retain standard attention or remove attention entirely, so the two ideas have not been effectively combined. We introduce LKAT (Linear Kolmogorov-Arnold Transformer) to close this gap: an isotropic ViT-style encoder that couples chunk-wise Gated Linear Attention with a two-layer KAN feed-forward block, backed by an I/O-aware fused RBF-KAN kernel to make radial-basis grid functions efficient in practice. Under a shared DeiT-style training recipe, LKAT-B outperforms ViT-B/16, ViT-5-B, and Mixer-B/16 on ImageNet-100, while Tiny, Small, and Base variants scale consistently on CIFAR-10/100. ImageNet-100 pretraining also transfers effectively to CIFAR fine-tuning, suggesting that gated linear attention and KAN-based radial basis functions provide complementary inductive biases for mid-scale visual representation learning. Code: https://github.com/mehizelali/linear-kan-transformer

We study the proper geometric dimension of full mapping class groups of non-orientable surfaces with punctures. Building on the computation for closed non-orientable surfaces, we prove that the proper geometric dimension agrees with the virtual cohomological dimension in all but a finite collection of low-complexity cases, for which we obtain explicit bounds. Our results provide the non-orientable counterpart of the corresponding computations for mapping class groups of closed and punctured orientable surfaces.

To elucidate the meaning of holographic entropy inequalities (beyond subadditivity) which characterize the entanglement structure of geometric states in holography, arXiv:2309.06296 proposed the "tripartite form" for these inequalities, consisting of tripartite information and conditional tripartite information terms with unit coefficients. While this provides a compact and useful packaging of the inequalities, it is not a priori guaranteed that all inequalities can be recast in this form. Here we conjecture that they can, and present substantial evidence, by proving that the two known infinite families of holographic entropy inequalities found in arXiv:2309.15145 can indeed be written in the tripartite form. This is significant because such recasting is particularly nontrivial for these families. Apart from providing the explicit tripartite form expressions for every member of these two infinite families, we detail how we arrived at them, in the process deriving several useful identities which may serve as stepping stones to formulate further repackaging of the corresponding information quantities. We also illustrate the power of the tripartite form by proving a number of structural properties satisfied by any holographic entropy inequality.

Locally recoverable codes (LRCs) combine global error correction with the ability to repair a small number of erased coordinates by accessing only a limited number of other coordinates. Motivated by their quantum counterparts, we construct several families of optimal cyclic $(r,\delta)$-LRCs that are Euclidean or Hermitian dual-containing. In the Euclidean case, we obtain four families of optimal dual-containing cyclic $(r,\delta)$-LRCs over $\mathbb{F}_q$ with a range of minimum distances extending beyond the local distance $\delta$. In the Hermitian case, we derive analogous families over $\mathbb{F}_{q^2}$ that are Hermitian dual-containing, when $(r+\delta-1)\mid(q^2-1)$. In addition, we develop a distinct construction for the case $(r+\delta-1)\mid(q^2+1)$ using symmetric defining sets and odd $\delta$, which yields optimal codes with minimum distances $\ell+2$, $\delta+2$, $2\delta-2$, and $2\delta$. The Euclidean Calderbank-Shor-Steane (CSS) and Hermitian stabilizer constructions then give corresponding quantum cyclic $(r,\delta)$-LRCs over~$\mathbb{F}_q$. Further, the resulting stabilizer codes are pure; they meet the relevant quantum Singleton-type bound, and are therefore optimal. We also provide a comparison with previous works, highlighting the parameter regimes and minimum distance ranges covered by our results that are not attained by existing constructions. Explicit examples illustrate the constructions and verify the dual-containment and purity conditions.

We develop a unified algebraic approach to spin-boson transformations based on the formalism of $f$-deformed oscillators. In the single-mode case, we show that the Holstein-Primakoff and Dyson-Maleev transformations, together with the interpolating $\alpha$-family, arise as different factorizations of the same algebraically determined object. The standard spin-boson mappings can thus be interpreted as realizations of a common structure, which makes it possible to clearly separate the exact algebraic content on the physical subspace from effects associated with non-Hermiticity, the choice of metric, and extensions beyond the physical subspace. In the two-mode case, the same approach yields both deformed versions of the Jordan-Schwinger transformation and new exact two-mode realizations. Our results provide a unified description of known spin-boson transformations and naturally lead to new bosonic representations.

We investigate gravitationally generated entanglement in two quantum harmonic oscillators induced by quadratic (Stelle) gravity, including corrections up to $1.5$ post-Newtonian order. Starting from the quadratic action, we derive the effective two-body Hamiltonian for two harmonically trapped masses, incorporating the contributions of the massive spin-$2$ ghost ($m_2$) and massive spin-$0$ ($m_0$) degrees of freedom of the gravitational field. For two quantised oscillators prepared in their ground state, we compute the von Neumann and Rényi entropies of the reduced state and identify a frequency at which the gravitationally-induced entanglement vanishes due to cancellation between relativistic momentum squeezing and quantum-delocalisation-induced position squeezing. We further analyze the cancellation frequency and derive the approximate constraint $m_0 < \sqrt[3]{4}\, m_2$ for the spin-$2$ and spin-$0$ modes. This relation follows from demanding a stable harmonic oscillator description. Finally, we study gravitationally-induced concurrence in a non-Gaussian setup and show how quadratic gravity modifies the entanglement generated between two spatial superpositions. The concurrence can approach $\mathcal{O}(1)$ for certain choices of mass, spatial superposition, particle distance, and spin-$2$ and spin-$0$ modes. The concurrence will deviate from Newtonian gravity at certain particle separations, depending on the energy of the spin-$2$ and spin-$0$ modes. For example, spin modes as low as $0.0197$ eV become distinguishable from Newtonian gravity at a distance $d \sim 40 \mu$m. This allows us to constrain the spin-$2$ and spin-$0$ masses in experiments.

Autonomous navigation requires precise and efficient semantic segmentation, yet existing frame-based approaches remain limited by motion blur, glare, latency, and the low temporal resolution (20-30 FPS) of conventional cameras, which leads to information loss between frames. Event cameras have emerged as an alternative sensing modality, capturing intensity changes asynchronously with high temporal resolution, high dynamic range, and sparse outputs. However, event-based algorithms still fall short of frame-based ones in accuracy, as most segmentation methods are designed for dense frame data. To overcome these limitations, we propose a hybrid vision architecture that combines conventional frame-based and event-based cameras. The system integrates two complementary components: (1) a compact Spiking Neural Network (SNN) with 42k parameters for motion estimation, and (2) a lightweight event-driven SNN with 0.84M parameters for frame-based semantic segmentation, which interpolates motion between frames to refine segmentation results. By predicting inter-frame segmentations, the framework achieves segmentation rates of up to 500 Hz with an energy consumption below 1.87 mJ per inference, while maintaining real-time GPU execution at frequencies up to 200 Hz. Additionally, our approach compensates for information loss in frames affected by blur or overexposure, enabling more robust perception in challenging conditions.

We establish conditional limit theorems, pointwise in the initial state, for absorbing Markov chains on a compact metric space $M$. We assume $L^1(M,\rho)$-continuous transition densities, irreducibility and aperiodicity. For the observable $f_\beta(x)=d_M(x,x_0)^{-\beta}$, with suitable $x_0$ satisfying $\rho(B_r(x_0))\sim C_d(x_0)r^d$, we prove that the point-process of normalised observations converges to a Poisson random measure. This yields totally right-skewed $\alpha$-stable laws for $\alpha=d/\beta\in(0,2)$ and, at the boundary value $\alpha=2$, a Gaussian limit with the non-standard normalisation $\sqrt{n\log n}$. We also establish a conditional central limit theorem for $L^2$ observables, exponential deviation bounds for bounded observables and a conditional Poisson law for visits to shrinking targets. The results and remarks have been formalised in Lean~4.

We study variation functions of some lacunary series along the sequence of $b$-adic partitions, where $b>1$ is an integer. By such a lacunary series, we mean that in the definition of the well-known Weierstrass function, the Lipschitz continuous cosine and sine functions are replaced by a continuous and piecewise continuously differentiable periodic function whose Fourier series has zero $(jb)^{\mathrm{th}}$-Fourier coefficients for all non-zero integers $j$. In the proofs, we use a probabilistic approach applying a martingale central limit theorem. Our result extends some recent results of Han, Schied and Zhang (2021), and can be applied when one chooses the periodic function in question, for example, as the Takagi function, a Weierstrass function or a certain lacunary series itself.

The aggregation of many lay estimates often outperforms individual expert judgment, a phenomenon known as the wisdom of crowds. While this is usually attributed to the independence of estimates, an even stronger effect arises through deliberation: averaging the consensus estimates of small deliberating groups outperforms the classical wisdom of crowds, with individual judgments themselves also becoming more accurate after deliberation. Whether these improvements transfer to large language models deliberating amongst themselves is unknown. Here we adapt a three-stage deliberation paradigm previously used with human participants for use with large language models from three different families, and test it across four domains of increasing real-world stakes: visual numerical estimation (Study 1), peer review of machine-learning papers (Study 2), detection of hidden malicious behavior by an artificial intelligence agent (Study 3), and sports forecasting against a real prediction market (Study 4). Across domains, deliberation reduced collective error beyond passive aggregation of independent responses, and post-deliberation individual judgments retained this collective gain. Notably, the advantage required model diversity: groups composed of clones of a single model did not benefit from deliberating. These results establish machine deliberation as a general-purpose aggregation mechanism, and point to diversity as an active ingredient.

We present an equation-free method for maintaining a dynamical system operating in a desired regime, even as system parameters are disturbed in such a way that qualitatively different dynamics would emerge. This method allows for real-time identification of changes made to a system's evolution equations induced by the parameter changes. If the equations governing the original system's dynamics are known, our method can allow one to determine the values of the parameters in real time. We illustrate our method with numerical examples using a reservoir computer control implementation.

This study introduces a decision-epoch-based dynamic electric autonomous dial-a-ride problem (Dyn-EADARP), in which incoming requests are collected and processed at periodic decision epochs. A key decision is not only how to serve requests, but also when to dispatch them. At each decision epoch, the service provider decides which requests to serve and which to postpone, while jointly determining vehicle routes, schedules, and charging decisions. Unexecuted parts of existing plans can be revised as new information becomes available. To solve this problem, we develop an ML–CO policy following the combinatorial optimization augmented machine learning (COAML) framework, which combines a statistical model with a combinatorial optimization layer for decision making. The statistical model predicts prizes for available requests, and a prize-collecting E-ADARP uses these prizes to jointly determine request selection, routing, scheduling, and charging. The statistical model is trained directly to improve the decisions produced by the optimization layer. Computational experiments on 320 test instances demonstrate the efficiency of ML–CO, which solves instances with nearly 500 requests in about 6 seconds on average. It achieves 8.7%–14.3% lower objective values than benchmark policies and an average gap of 4.8% to the anticipative reference. The results provide several managerial insights. First, serving requests immediately is not always best, as selectively postponing some requests can create better ride-sharing opportunities. Second, revising existing plans preserves operational flexibility and substantially improves solution quality. Finally, more frequent decision making does not necessarily improve performance, highlighting the importance of choosing an appropriate decision frequency.

In recent years, there has been a surge of interest in Cultural NLP, with substantial efforts to create globally inclusive NLP systems. The rapid growth of literature in this field makes it difficult to track trends in methods and data resources. To address this, we analyze over 375 papers to answer three complementary questions: (1) What Cultural Capabilities (CCs) are being targeted in NLP systems? (2) How are cultural data resources being created? and (3) What methods are being used to improve the CCs of those systems? We discuss trends observed across the three questions, and identify relevant research gaps. To facilitate further research in this field, we release our full list of analyzed papers in the form of an interactive web interface, which includes a feature to allow researchers to add their work; we hope this facilitates future research and proves to be a valuable resource for the Cultural NLP community.

This paper presents a stacked two-layer force-sensing resistor (FSR) array designed for robotic fingertips that combines high-resolution pressure mapping with shear-force estimation. A compliant lattice elastomer spacer converts shear loading into a measurable inter-layer displacement, producing relative center-of-pressure (CoP) shifts between layers. A physics-based moment balance links inter-layer CoP displacement to shear force, while an end-to-end CNN–GRU model captures nonlinear effects from load-dependent compression and contact redistribution. This model, with both layers as input, achieves coefficients of determination $R^2 = 0.914$ for $F_x$ and $R^2 = 0.944$ for $F_y$, consistently outperforming single-layer baselines for shear-force estimation. Robotic manipulation experiments show that, for contact-motion tracking, the deep layer tracks the translation and rotation imposed by the robot arm, whereas the superficial layer tracks the slip at the contact surface. Transient changes in the difference between the total pressure responses of the two layers provide the best slip-event detection performance among the tested cues. These results demonstrate that two-layer FSR arrays can provide three-axis force estimation, contact-motion tracking, and slip-event detection beyond conventional normal-force sensing.

The lifetime of the strong magnetic field generated in relativistic heavy-ion collisions remains one of the major open questions in the study of the quark–gluon plasma. We propose heavy-quark spin precession as a probe to quantify the magnetic field and its profile in such collisions. We investigate the Larmor evolution of polarized charm and bottom quarks propagating through an expanding quark–gluon plasma in the presence of the magnetic field. We show that realistic magnetic-field strengths and lifetimes generate measurable accumulated precession phases prior to hadronization, leading to characteristic charge-dependent polarization splittings between $\Lambda_c^+$ and $\bar{\Lambda}_c^-$, as well as between $\Lambda_b^0$ and $\bar{\Lambda}_b^0$, through the mixing of transverse and longitudinal polarization components. The predicted signals exhibit distinctive transverse-momentum and quark-mass dependence, providing complementary sensitivity to the magnetic-field lifetime in the charm and bottom sectors. Our results suggest heavy-flavor polarization, especially in the charm sector, as a quantitative probe for the space–time evolution of magnetic fields in relativistic heavy-ion collisions.

We present a candidate counterexample to a conjecture stating that the existence of a Lyapunov-Krasovskii functional with a pointwise dissipation rate is sufficient for the input-to-state stability of time-delay systems. The counterexample has been derived through interactions with large language models.

A workflow is introduced for constructing accurate, wavefunction-derived Kohn-Sham (KS) exchange-correlation (XC) energies across atomic and molecular species. Correlated total energies and densities are obtained from configuration interaction wave functions in a polarized triple-zeta basis, cc-pVTZ, and each wavefunction density is then mapped onto a KS determinant. A composite correction adds valence and core basis functions (cc-pVQZ and cc-pCVTZ), plus a two-point Riemann extrapolation to approach the complete-basis-set limit. The workflow is applied to 100 closed-shell atomic and molecular species composed of main group elements to form the XC100 data set. The resulting KS densities closely reproduce the correlated densities, with a median L2/Ne difference of 1.42 X 10^{-5}, while the composite corrections recover substantial correlation energy beyond the cc-pVTZ reference. Comparison with conventional and machine-learned density functional approximations gives insight into the quality of Exc across different types of models for XC. In all, this paper's workflow demonstrates a practical route for generating XC reference data for the assessment and development of density functionals.

We present high angular-resolution ($\sim 0.{''}1 - 0.{''}5$) ALMA observations of millimeter-wave line and continuum emission (at $\sim0.44$ and $0.88$ mm) in the pre-planetary nebula IRAS 06530–0213 (IRAS 06530). These data show the presence of an extended circular ring – first evidence of the last thermal-pulse preceding the post-AGB phase in a carbon star – and a central bipolar nebula (CBN) and torus. The mass-loss rate of IRAS 06530's AGB progenitor decreased immediately after the thermal pulse, then rose again just before the post-AGB phase as evidenced by the presence of filamentary arc structures around the CBN. The arc stuctures are likely part of a 3-D Archimidean spiral structure generally attributed to the presence of a binary companion. But we do not find a compact continuum source at the location of IRAS 06530's central star, such as that associated with the compact dusty disks typically found in disk-prominent post-AGB objects known to have binary companions. The expansion ages derived for the torus and CBN imply that IRAS 06530's progenitor transitioned to a post-AGB star $\lesssim700$ yr ago. The molecular mass of the ejecta in IRAS 06530 is dominated by the filamentary arc region with a mass $M_{H_2}=(0.12-0.25) M_{\odot}$. Compared with solar values, the torus of IRAS 06530 appears to be significantly (modestly) enriched in $^{13}$C and $^{17}$O ($^{15}$N) as well – a pattern of rare-isotope enrichment inconsistent with standard nucleosynthesis models. From the luminosity of IRAS 06530 and the age of its detached shell, while it was still on the AGB, we infer that the mass of IRAS 06530's progenitor was $(1.6-3.4) M_{\odot}$.

JWST has facilitated the detection of faint, auroral emission lines needed to directly measure the electron temperature and elemental abundances in high-redshift galaxies. However, such measurements still require substantial observational investment, potentially making self-consistent, population-level studies of direct-method metallicity scaling relations across multiple epochs of Cosmic time prohibitively expensive. Photoionization modeling could allow us to measure metallicity using more routinely-observed emission lines across larger galaxy samples with shallower spectra. We use $z\sim 2$ galaxies from the CECILIA survey and local galaxies and H II regions from the LBT $Y_P$ Project to compare abundance measurements made via the $T_e$ method to abundances estimated using the novel photoionization modeling code, Cue. Based on the results, we explore the viability of, biases introduced by, and the best practices for measuring gas-phase metallicity with photoionization modeling. We show that Cue can be used to accurately measure O/H while remaining agnostic to the ionizing spectrum and that accurate recovery of O/H can be achieved with relatively bright oxygen and sulfur lines, demonstrating that Cue could be used to measure metallicity in large samples that lack the depth necessary for direct measurements of O/H. However, using sulfur emission lines can also severely bias the results of photoionization modeling in high-redshift galaxies, where non-Solar abundance patterns are common. We make recommendations regarding the use of photoionization models to measure metallicity in local and high-redshift samples and future developments to photoionization modeling methods.

Matrix-valued optimizer states may contain relational structure that is not captured by treating their entries independently. We study whether relations within matrix-valued optimizer states can be exploited to improve optimization. To this end, we introduce a unit-relation-transform abstraction and instantiate it as COREM, a Cosine-Relation Momentum Reshaping method with stateful writeback. COREM partitions the momentum state into update units, computes cosine relations among them, and uses these relations to reshape the momentum before writing the transformed state back to the optimizer. This stateful mechanism allows the reshaped momentum to affect not only the current update but also future optimization dynamics. We evaluate COREM on CIFAR-10 with an MLP and on enwik8 with a Transformer. Compared with Muon, COREM shows lower early-stage step efficiency but stronger improvement in the mid-to-late stages of training, achieving better final validation performance on CIFAR-10 and comparable final performance on enwik8. Spectral diagnostics on enwik8 show that COREM consistently increases entropy effective rank and reduces the concentration of singular energy in dominant modes, while preserving an anisotropic spectrum. For square matrix updates, COREM requires approximately 13.3% of the transformation FLOPs of Muon with five Newton-Schulz iterations.

Large language models (LLMs) increasingly ground their answers in proprietary data and live web content through both single-shot retrieval-augmented generation (RAG) and multi-turn agentic search. Yet the web path they use was built for human readers: search services return URLs and snippets ranked by generic relevance, and content delivery networks (CDNs) cache URL-addressed objects without knowing which passage an agent needs. LLMs instead consume short, semantically coherent passages - hereafter, chunks - selected for downstream utility rather than similarity alone, retrieve statefully across reasoning turns, and, as uncoordinated streams, repeatedly fetch, clean, chunk, and embed the same content. We argue that semantic chunk retrieval should become a first-class network-delivery abstraction, and propose the Semantics Delivery Network (SemDN): an origin-authorized, hierarchical substrate that indexes, searches, and caches web content at chunk granularity, serving clients and origins alike. SemDN is more than finer-grained caching: it must estimate missing or stale evidence without an explicit miss signal, let clients choose retrieval representations that origins need not see, and share state among clients with the same representation. Preliminary results show that page-first retrieval processes two to three orders of magnitude more content than agents consume, that agentic queries exhibit task-local chunk reuse invisible to URL caches, and that chunk delivery improves answer quality per context token. We organize an open research agenda around shareable retrieval state, hierarchical caching and refresh under coverage risk, and deployability, including incentives, privacy, and verifiability. Our code is available at: https://github.com/sarendis56/SemDN_HotNets26

Let $n,d\geq1$, and suppose that $E\subset \mathbb{Q}_p^n$ contains a degree-$d$ polynomial image of $\mathbb{Z}_p$ in every leading direction of a nonempty set $V\subset\mathbb{P}^{n-1}(\mathbb{Q}_p)$. We prove the sharp bound $\dim_H E\geq\dim_H V+1$. For joint block-valued polynomial evaluations, the total incidence dimension is at least one plus the supremum of the image dimensions. For analytic coefficient sets, Haar-almost every evaluation attains this supremum, and we bound the Hausdorff dimension of the parameters where the image dimension drops. For bounded coefficient sets and arbitrary fixed anisotropic block scales, we prove a quantitative covering comparison with a common Haar-null exceptional set. Outside this set, each evaluation's covering number dominates the maximum over any compact reference ball, up to any positive power loss at all sufficiently small scales. The proofs use the polynomial-to-line lifting map due to Nadjimzadah, together with Dhar's prime-power Kakeya set estimate and a tube maximal inequality derived from it.

We investigate whether adding $t$, the positive magnitude of the squared nuclear four-momentum transfer, enables boosted decision trees (BDTs) to improve invisible-dark-boson selection relative to optimized rectangular cuts at the Electron-Ion Collider. We model coherent exclusive scalar and vector production at generator level in electron-gold collisions at 18 GeV by 100 GeV per nucleon. Both methods use identical weighted samples, inputs, preselection, and optimization objectives. Using only electron information, the BDT provided no consistent advantage over optimized cuts for signal selection across 11 masses for each boson type. When both methods also use $t$, the BDT distinguishes signal from background slightly better than optimized cuts at 10 GeV for both boson types. These results motivate further investigation of machine learning in EIC dark-boson searches through exclusive processes where $t$ can be reconstructed.

Robotic ultrasound (US) calibration is essential for accurately relating US images to the robot coordinate system, but accurate and automated calibration remains challenging because existing methods often require complex phantoms or external 3D trackers. In this work, we develop a tracker-free robotic US calibration framework using a spherical-marker phantom and a highly automated perception pipeline for sphere-center localization. The proposed threshold-free image-processing method localizes the spherical feature based on each US image's intensity distribution, eliminating hand-tuned intensity thresholds and improving robustness across imaging settings without per-system retuning. Multi-pose observations of the spherical fiducial are then used to estimate the US-to-EE transformation without external tracking or prior localization of the sphere center in the robot base frame. We validate the proposed framework on a robotic US platform through repeated sphere scans and further assess the calibrated system using geometrically distinct phantoms with known CAD models. Across 12 cross-validation folds, single-marker calibration achieved sphere-center accuracy and precision of $1.75\pm0.51$ mm and $0.85\pm0.11$ mm, respectively, compared with $1.72\pm0.51$ mm and $0.84\pm0.12$ mm for three-marker calibration. Across the three reconstruction sets, the single-marker calibration yielded pooled post-registration point-to-surface MAE$\pm$SD values of $0.41\pm0.35$ mm for the cone and $0.50\pm0.41$ mm for the triangular prism, closely matching the three-marker results of $0.40\pm0.35$ mm and $0.48\pm0.40$ mm, respectively.

We investigate the dynamics of charged particles and fields in the background of a charged black hole in bumblebee gravity, aiming to better understand the role played by the Lorentz-violating parameter $l$. We first review the derivation of the charged bumblebee black hole and investigate its main physical and geometrical properties. We then obtain the circular and bound trajectories of charged particles and find that the innermost stable circular orbit increases with $l$. By using a numerical approach, we compute the total absorption cross section for arbitrary values of the scalar wave frequency $\omega$. Since the spacetime is not asymptotically flat, we construct the total absorption cross section by taking into account the modified asymptotic momentum and flux. Analytical approximations are derived in the low- and high-frequency regimes. The low-frequency expression displays a transition velocity that separates two distinct asymptotic branches and generalizes the corresponding Reissner-Nordström result. Our numerical results for the cross section agree with the analytical approximations in their corresponding limits, and the absorption parameter space can be divided into three regions: Unbounded absorption, bounded absorption, and bounded superradiance. In particular, superradiance occurs whenever $\omega<\omega_{c}$, where $\omega_{c}$ is the threshold for superradiance. Moreover, the superradiance amplification decreases as we increase $l$, and charged bumblebee black holes with $l < 0$ lead to greater superradiant scattering than in the Reissner-Nordström case. We also note that although increasing $l$ lowers the potential barrier, it reduces the total absorption cross section because of the geometrical factor $1/(1+l)$ present in the cross section formula.

Second-order methods for smooth monotone variational inequalities reach the optimal rate $O(T^{-3/2})$, but a distributed exact Jacobian costs $d$ times more communication than an operator value. We show that similarity does part of the work for free: if the server's Jacobian differs from the global one by at most $\beta$, using it gives $O(L_1D^3T^{-3/2}+\beta D^2T^{-1})$ at first-order communication cost. A quasi-Newton approximation of the residual Jacobian $\nabla F-\nabla F_1$, built from secants already communicated, improves the model but cannot remove the $T^{-1}$ term, because any uniform bound on the Jacobian error leaves it in the rate. We therefore certify the surrogate only along the candidate step: one Jacobian-vector product tests it, and a failed test is reused as an exact correction. This attains the exact rate $O(L_1D^3T^{-3/2})$ while transmitting only vectors. Experiments on LIBSVM and synthetic instances measure accuracy against communication.

Cosmic rays (CRs) escaping collisionless shocks form a dilute, relativistic population whose current amplifies the upstream magnetic field, a process widely attributed to the non-resonant (Bell) instability. Solving the dispersion relation for both cold and finite-spread CR distributions, we show that for the maximum-energy escaping population, the resonant mode can outgrow the non-resonant mode. At slower shocks, this dominance persists for broader CR distributions, and sufficient pitch-angle broadening can even stabilize the non-resonant mode while leaving the resonant mode unstable. Relativistic hybrid particle-in-cell simulations confirm the cold-beam linear theory predictions and, in the nonlinear regime, saturate at $\delta B/B_0 \sim 1$ with significant pitch-angle redistribution. Neglecting the resonant instability thus underestimates magnetic field growth at the very scale needed to confine the highest-energy escaping CRs.

We address the problem of recovering high-speed videos from dynamic scenes under extreme photon sparsity. Existing methods rely on aggregating photon detections in local spatiotemporal windows to improve signal-to-noise ratio; however, this local grouping discards global structure and fails in low-light regimes where photon detections are sparse in space and time. In this work, we show that the information needed to recover both motion and illumination is encoded in correlations over the full space-time pattern of photon arrivals. Building on this insight, we develop a spatiotemporal flux probing theory and an algorithm that estimates the Fourier coefficients of the underlying intensity directly from the photon stream. We demonstrate that our approach (1) recovers fast motion and temporal illumination dynamics with substantially fewer photons than prior methods, (2) enables velocity-selective videography that automatically refocuses video onto specific detected motions, and (3) generalizes across sensing modalities including single-photon, event, and spike cameras.

Behavioural evaluations of hosted language models can vary because the evaluated service, the measurement instrument, or both differ across runs. We separate three validation questions: whether a prior finding recurs on fresh data under its historical configuration (replication), whether the endpoint changes when the evaluation-and-inference configuration is rebuilt under the same identifier (measurement sensitivity), and whether the finding persists across subsequently tested identifiers under one common instrument (persistence). We study these questions in Regent Chess, a sequential environment in which a hidden, mutable state is recorded exactly, allowing stated beliefs to be scored against ground truth at action time; positive endpoint values mean worse performance than a matched-uniform comparator. The previously reported Gemini 3.1 Flash-Lite deficit recurs on fresh games under its historical configuration (+0.0530, 95% CI [+0.0329,+0.0714]). In a back-to-back same-day H/R comparison under the same public identifier, the model-minus-uniform endpoint is 0.0429 lower under the rebuilt configuration (95% CI for the H-minus-R contrast [+0.0182,+0.0667]); all six configuration components vary jointly, so no component is isolated. Under rebuilt R, the prospectively frozen, interleaved same-window 4K comparison reverses sign between Gemini 3.1 and Gemini 3.7, identifiers that differ in release and product tier; additional descriptive and exploratory cells show the same directional pattern. Any additional serving-period contribution remains unresolved (-0.0166, [-0.0483,+0.0157]). Replication, measurement sensitivity, and persistence can therefore yield different conclusions within one evaluation, motivating explicit indexing of hosted-model behavioural claims by tested identifier, serving period, measurement instrument, and inference configuration.