Papers

We consider a variation of the Cohomological Rigidity Problem: whether two quasitoric manifolds whose cohomology rings are isomorphic are homotopy equivalent. We show that if two quasitoric manifolds have isomorphic cohomology rings and the associated polytope of one of them is a product of simplices, then they are homotopy equivalent after localizing away from an explicit list of primes.

Binary classification often requires controlling both type I and type II error rates at prespecified levels. When the class distributions overlap substantially, the two error limits may be incompatible if every observation must be classified. We study Neyman-Pearson classification with indecisions (NPI), which permits uncertain observations to remain unclassified and assesses selective type I and type II errors among definitive classifications within each class. For an independently trained score, we develop a model-free calibration procedure that combines all candidate threshold pairs passing calibration into a rule whose decision region contains that of every passing candidate. We couple the entire threshold search to a common martingale within each class and compute its finite-horizon crossing probability exactly, avoiding a multiplicity adjustment for the number of candidate pairs. The resulting classifier satisfies both population selective error limits simultaneously with user-specified high probability in finite samples, without assumptions on the accuracy of the fitted score. We bound the additional indecision due to calibration and evaluate the procedure in simulations and applications to recidivism and credit-default prediction.

Branched flow of light arises when spatially correlated disorder folds families of rays into caustics. Here, we demonstrate a temporal analog in the retarded-time coordinate of an optical pulse in a waveguide, where branched flow becomes hyper-dispersive. Retardation during pulse propagation induces spatiotemporal correlations that break propagation reciprocity and imprint a trajectory memory. This nonreciprocity enables unidirectional temporal branched flow with no spatial counterpart. A memory model is developed combining ray-density and phase fluctuations with single-ray dynamics in a memory cell. The model reveals competition between fluctuation-induced focusing and destruction, which yields nontrivial diagrams of propagation regimes with distinct dispersion scalings. For a 532-nm pulse in a $\mathrm{LiNbO_3}$ fiber, we predict that refractive-index disorder induced by active modulations or quantum vacuum fluctuations can produce first caustics on meter-to-kilometer scales, offering routes to experimental observation and to sensing ultra-weak fluctuations.

Humanoid whole-body controllers can now track a diverse set of dynamic motions, but they are typically trained offline and then frozen, so teaching such a controller a new skill tends to erode the skills it already mastered. We study continual learning for humanoid whole-body motion, where a single controller must acquire skills from a sequential task stream without revisiting past data. We introduce Similarity-guided LoRA-PNN, a progressive neural network (PNN) policy that prevents catastrophic forgetting by construction while reusing knowledge across skills through lightweight low-rank adaptation. A two-level motion-similarity measure, built from dynamic time warping aggregated by optimal transport, decides which prior skill to build on and how much new capacity to allocate, yielding strong forward transfer and large efficiency gains. Across six sequentially learned skill categories, our similarity-guided LoRA policy attains the best forward transfer (0.125 vs. 0.079) and the highest average accuracy among all methods, while saving up to 94.5% of trainable parameters and 40.8% of training time. The resulting controller reaches 96.13% sim-to-sim transfer and is deployed on a physical Unitree G1. Our code is available at https://anonymous.4open.science/r/continual-humanoid-learning-35D3.

Quantum sensing is emerging as a practical means of improving sensing capabilities in consumer electronics, particularly where size, power, and noise constrain classical approaches. In this paper, we reviewed the near-term applicability of quantum sensing using a platform-and-application framework. Within this framework, we outlined the general sensing protocol and discussed the working of the four key quantum sensing platforms relevant to consumer electronics: nitrogen-vacancy (NV) centers, atomic vapor cells, Rydberg atomic sensors, and photonic quantum sensors. Through case studies involving navigation and positioning, healthcare and wearables, radio-frequency (RF) and wireless systems, the Internet of Things (IoT), and imaging, we examined the tangible engineering advantages offered by quantum sensing. Rather than replacing devices outright, quantum sensing is more likely to earn its place in the near-term by upgrading specific measurement components within hybrid classical-quantum systems. Right now, the clearest opportunities are in weak-field detection, compact RF reception, and sensing that remains robust in noise.

Reservoir computing (RC) offers an efficient data-driven approach for forecasting extreme events (EEs), which correspond to rare and large-amplitude dynamical occurrences. We propose a dual-stage cascade framework that jointly predicts both the timing and peak intensity of upcoming EEs. A traditional RC branch integrates long-term precursor dynamics to support stable detection and long-horizon prediction, while an NGRC branch captures local nonlinear waveform geometry to improve fine-grained time-to-peak localization and complement peak-intensity estimation. The fused features then feed a ridge classifier that issues a binary alarm upon detecting precursors. Only then do two ridge regressors, trained on true-positive snapshots, estimate time-to-peak and peak intensity. This classify-then-regress design addresses severe class imbalance without data resampling. Evaluated on simulated pump-modulated VCSEL data, the hybrid model achieves a SEDI value >0.8, with MAEs around 0.2 ns and 0.2 a. u., maintaining performance up to a 20 ns warning horizon. The framework advances extreme-event forecasting from binary warnings to fully quantitative dual-objective prediction.

Shininess is one of the main theory combination methods in Satisfiability Modulo Theories. We present two infinite families of generalizations of it: one involving a property between gentleness and shininess, which helps us see gentleness itself as a variation of shininess; and another having no further computability requirements on the weaker theory, in addition dropping the need for smoothness. We prove these methods sharp, and compare them with existing methods.

Open-pit mining operational planning involves allocating limited resources while satisfying production, equipment, and ore-quality requirements. Existing approaches often assume deterministic ore grades or rely on simulation-based evaluation under uncertainty. In this paper, we propose a chance-constrained bi-objective formulation of the open-pit mining operational planning problem under uncertain ore grades. We aim to maximize ore production and minimize fleet cost while satisfying stochastic quality requirements through chance constraints. We model ore grades as independent normally distributed random variables and derive a deterministic reformulation of the two-sided chance constraints, avoiding sampling or simulation during fitness evaluation. We evaluate four multi-objective evolutionary algorithms on benchmark instances under different levels and structures of uncertainty. Our results show that NSGA-II and NSGA-III generally obtain the best feasible ore-production values, with NSGA-II requiring less computational time. GSEMO has the lowest computational cost but obtains feasible solutions less consistently and generally provides lower solution quality. We also observe that higher confidence and uncertainty levels reduce feasibility, with the effect depending on the uncertainty structure. The results highlight the importance of considering both the magnitude and structure of uncertainty in short-term open-pit operational planning.

LoRA-based continual learning methods mitigate catastrophic forgetting through various mechanisms, yet nearly all complement these with small learning rates as a heuristic to restrict gradient scaling magnitude. Such fixed heuristics lack theoretical guidance on how the strength of this restriction should evolve as tasks accumulate. We reveal that even under directional constraints such as nullspace projection, finite-precision updates inevitably leak into the subspace of accumulated prior knowledge along multiple directions. While small learning rates attenuate such leakage, they cannot prevent the accumulated forgetting from intensifying as the effective rank of historical knowledge grows. We show that the optimal magnitude restriction should adaptively increase with this effective rank to balance stability and plasticity, i.e., preservation of previous knowledge and acquisition of new task information. Under an anisotropic leakage model, we derive a pacing law $s^*=\sqrt{R/c}$ that characterizes the optimal scaling of gradient steps, i.e., the magnitude restriction itself, where $R$ is the effective rank of past updates. Based on this insight, we propose PaLoRA, which compresses historical knowledge via adaptive SVD truncation, projects gradients onto the nullspace of prior tasks, and applies rank-aware adaptive pacing. Experiments demonstrate consistent improvements over prior methods, with particularly strong performance in long-horizon settings, achieving substantial gains of 4% accuracy on challenging 50-task ImageNet-A and ImageNet-R benchmarks.

Multimodal Large Language Models (MLLMs) have demonstrated strong performance in video understanding, yet efficiently processing long, high-resolution videos remains challenging. Such videos often contain substantial spatiotemporal redundancy, and processing redundant visual tokens can incur avoidable computational overhead. Many existing methods prune visual tokens during or after vision transformer (ViT) encoding, leaving much of the encoding cost unaddressed. Some approaches prune patches before encoding but rely on learned auxiliary networks for patch selection, incurring additional training and inference overhead. To address these limitations, we propose FlashGaze, a training-free method that reduces spatiotemporal redundancy before ViT encoding without introducing auxiliary networks. FlashGaze uses pixel-space differences as a proxy for information loss and employs Quadtree Dynamic Programming to jointly optimize patch dropping, merging, and keeping under a fixed budget. Experiments on two MLLM backbones across multiple benchmarks demonstrate substantial efficiency gains while largely preserving accuracy. On Qwen3-VL-8B, FlashGaze retains 98% of the full-input baseline accuracy on LongVideoBench while achieving up to 5.4x and 17x speedups in ViT encoding and MLLM prefill, respectively, and reducing peak GPU memory usage by a factor of 1.8. These efficiency gains enable the model to process videos with more frames and higher resolutions on the same GPU hardware, unlocking video understanding at scales previously out of reach.

Dielectric screening of electric fields is modified by interfaces and confinement, and any accurate description of interfacial chemistry necessitates properly modeling the nonuniform dielectric tensor. However, models with short range interactions, such as local machine learned interatomic potentials (MLIPs), are increasingly used in simulations of molecular interfaces without quantitative understanding of their nonuniform dielectric response. To build this understanding, we use the framework provided by local molecular field (LMF) theory to quantify the roles of short and long range electrostatics in confined water. Short and long range models predict the same transverse dielectric profile but short range models predict qualitatively different longitudinal dielectric profiles than their long range counterparts. To understand these differences, we develop a Landau theory that shows that long range interactions stiffen polarization fluctuations by a factor of the bulk dielectric constant and reduce the interfacial polarization correlation length by an order of magnitude. LMF theory, which captures long range interactions with an averaged field, can correct the structure and dielectric response, but the standard fluctuation relation no longer holds. We derive a fluctuation relation and integral equation for LMF theory and demonstrate their accuracy for predicting longitudinal dielectric response. MLIPs that incorporate interfacial configurations in their training essentially learn a static mean field correction at the interface, such that the integral equation can be used to predict their nonuniform dielectric profile from polarization fluctuations. We also show that short range MLIPs can be combined with symmetry preserving mean field (SPMF) theory to provide a linear-scaling alternative for long range interactions and predicting nonuniform dielectric functions.

A common empirical strategy in triple-differences (DDD) is to include either covariate trends or covariate levels to a three-way fixed effects (3WFE) regression. This strategy is typically motivated by the conditional parallel gaps assumption which assumes that deviations from parallel trends are similar among units with comparable observed covariates. We formally study both 3WFE specifications and show that, in general, neither consistently estimates the average treatment effect on the treated (ATT). Our diagnosis has two parts. First, we show that the OLS estimands of both specifications fail to satisfy the covariate balancing condition that is sufficient for them to equal the ATT. Second, we characterize the additional assumptions for each OLS estimand to equal the ATT. To address these limitations, we propose a matched triple-differences framework that accommodates a general class of matching procedures, including nearest-neighbor matching and kernel matching. Within this framework, we construct a class of consistent matching estimators, establish their asymptotic normality, and provide a consistent variance estimator that accounts for the variability introduced by the matching step. Our empirical application shows that the proposed matched triple-differences estimator can yield estimates and qualitative conclusions that differ from those obtained using the 3WFE regression.

Life support equipment coupled to the human lungs forms a complex, nonlinear dynamic system. Current respiratory mask test standards rely on sinusoidal breathing machines and surrogate trachea geometries that substantially reduce physiologically relevant airway inertance. This paper shows that the ISO 16900-5 trachea does not generate physiologically meaningful exhalation momentum, limiting the ability of standard test configurations to reveal valve dynamics relevant to human use. A physiologically motivated “lip-nozzle” surrogate is introduced as a diagnostic tool to restore realistic momentum transfer, enabling observation of exhalation behavior that is not observable under existing test conditions. Nonlinear dynamic simulations incorporating this surrogate reveal a force-balanced operating regime in which exhalation-jet momentum can offset flow-induced valve resistance, in one representative case reversing exhalation mean effective pressure from resistive to assistive. This effect depends on the relationship between the valve's restoring force and lift, representing a design consideration relevant to future valve development. Implications for mask design, valve placement, and future test methods are discussed. This work does not propose new performance limits or acceptance criteria; rather, it demonstrates how current test fixtures suppress inertance- and momentum-driven effects that can materially influence exhalation valve dynamics.

The enhanced index tracking (EIT) portfolio selection problem aims to construct a portfolio that is expected to outperform a benchmark index. In practice, investors face uncertainty in the joint distribution of asset and index losses, as the true distribution is typically unknown and only partial information is available. Moreover, portfolio selection requires balancing the trade-off between mean loss and downside risk while targeting higher returns. Effectively modeling and managing these factors in EIT portfolio selection is therefore of both practical and research interest. To address these challenges, this paper proposes robust EIT portfolio selection models under distributional uncertainty, guided by Pareto-optimality theory. The models minimize a convex combination of worst-case mean loss and downside risk, subject to a constraint on worst-case mean return. Two uncertainty sets are considered: one assuming a known mean loss vector and covariance matrix, and a more general set with unknown moments. Closed-form solutions are derived for the former, while the latter reduces to tractable convex optimization problems. Empirical results based on real market data show that the proposed models outperform not only the tracked index but also the equally weighted portfolio, robust mean-variance models, and robust variance models in terms of out-of-sample cumulative wealth, as well as Sharpe, Sortino, and Omega ratios. Moreover, portfolios that minimize a convex combination of worst-case mean loss and downside risk consistently outperform those that minimize downside risk alone. We also provide practical guidance for selecting optimal weighting coefficients to effectively balance risk and return.

The neck, specifically the cervical spine, is a highly fragile and mobile part of the body with a high risk of catastrophic injury. Whether someone is injured on a battlefield, in a natural disaster, or in an athletic event, great care is always taken with the cervical spine when transporting, rolling, or moving the patient. In this work, we present an algorithm and adaptations for bi-manual robots to stabilize the cervical spine during rolling maneuvers. We investigate techniques to maximize grip strength within safety bounds and present a control approach for proper neck rotation. We found that with our approach, a bi-manual robot is capable of achieving human-level performance in maintaining target rotational alignments. The axial alignment for the robot with prediction was within .21 degrees of human novices.

The electric autonomous dial-a-ride problem (EADARP) extends the classical dial-a-ride problem by incorporating battery and charging constraints for electric vehicles. In practice, travel-time uncertainty can cause violations of time-window constraints. Large neighborhood search is effective for solving the EADARP, but its performance can depend on the choice of insertion operator during the repair phase. This paper investigates insertion-operator selection within a bilevel large neighborhood search framework for deterministic and chance-constrained variants of the EADARP. In the chance-constrained variant, arc travel times are modeled as independent normally distributed random variables, and upper time-window constraints are enforced probabilistically. We consider six selection methods, namely fixed greedy insertion, fixed regret-based insertion, random selection, a deterministic state-based rule, performance-adaptive ALNS selection, and LLM-based state-aware selection. Experimental results show comparable performance on smaller instances, while differences become more evident on larger and more constrained instances. There is no single strategy that performs best across all instances, and the relative performance of the LLM-based, rule-based, and ALNS strategies varies with the problem instance and experimental setting.

We formulate the gravitational field on maximally symmetric spacetimes as a gauge theory, and investigate higher-form symmetries of the linearized gravitational field via a series expansion in Newton's gravitational constant. To treat gravity as a gauge theory, the MacDowell-Mansouri formulation based on Cartan geometry is utilized. We show the existence of a 1-form symmetry in linearized gravity on Minkowski spacetime. Furthermore, for other maximally symmetric spacetimes (de Sitter and anti-de Sitter spacetimes) with a small cosmological constant, we demonstrate the existence of an approximate 1-form symmetry in the corresponding linearized gravity, detailing its explicit dependence on the cosmological constant.

Random assignment can make ordinary least squares (OLS) inference insensitive to outcome dependence, yet iid resampling can still fail because assignment and resampling need not remove the same covariance terms. With binary treatment, the iid variance target differs from the sampling variance by exactly minus aggregate cross-unit covariance of treatment effects. Under a Gaussian first-order limit, positive covariance leads to over-rejection and negative covariance to under-rejection. Two designs can generate the same distribution for each observation but require variance corrections of opposite signs, so no marginal-only variance correction is first-order exact for both. For first-order Gaussian inference, only one covariance component—the covariance carried by the randomized-regressor score—must be recovered. Standard dependence estimators on that score restore validity under suitable ordered or grouped dependence conditions. In simulations with ordered data, fixed-bandwidth calibration reduces several large-bandwidth size distortions.

Significance: RF-induced heating of endovascular devices limits MRI-guided interventions, including targeted drug delivery to brain tumors. Purpose: To present a tool that rapidly generates randomized guidewire trajectories for RF heating risk assessment. Methods: A MATLAB tool models the guidewire as a spline with randomized control nodes and a fixed nominal length. As a use case, tip sSAR was estimated for 1000 trajectories using straight-wire transfer functions and 64 MHz local and body coil fields (matched B1) in the Duke phantom. Results: Length accuracy was 99.84%, and 3000 trajectories were generated in 11.5 s. Body-to-local sSAR ratios at the 50th, 95th, and 99th percentiles were 1.5, 1.6, and 2.27, but some trajectories heated more under the local coil. Conclusion: The tool enables large-sample heating assessment, and coil type alone did not reliably predict individual trajectory risk.

Large language models (LLMs) can generate clinical narratives that are insufficiently grounded in patient-specific evidence. In traditional Chinese medicine (TCM), errors can propagate from etiology and pathogenesis through syndrome diagnosis and treatment principles to prescription generation. We developed TCMClinicalReason-Bench using 2,000 multicenter electronic health record cases to distinguish case-grounded responses from fluent but unsupported diagnostic and therapeutic conclusions. Five general-purpose and two TCM-specific LLMs were evaluated in zero-shot settings. An evidence-constrained rubric assessed seven diagnostic and therapeutic components and three cross-block relations, allowing case-supported alternatives. Qwen3.7-Plus with TCM retrieval served as the automated judge, alongside parallel blinded ratings by five senior TCM clinicians on a 600-case subset. Structural completeness was nearly saturated (99.3-100.0%), but normalized content scores ranged from 40.7% to 54.1%. The five general-purpose models averaged 50.0%, versus 41.3% for the two smaller TCM-specific models. Cross-block logic consistency ranged from 60.8% to 66.8% and correlated moderately with content across cases (Pearson's r = 0.515-0.656). Deficits were greatest in prescription generation, prescription analysis, and symptom-guided modification. In judge stress testing on 100 independent cases, perturbation detection rates across the three relations were 57%, 56%, and 31%, with contradictions detected more reliably than omissions. Separating component quality from cross-block consistency localizes failures missed by endpoint and completeness metrics and identifies where clinician oversight remains necessary.

We study iterated cotangent integrals with cyclotomic shifts and express their values along specified reference paths in terms of cyclotomic multiple zeta values. Differences of cotangent forms extend to a punctured projective line over a totally real cyclotomic field, giving a family of "real cyclotomic multiple zeta values." With rational tangential endpoints, these difference integrals are periods of mixed Tate motives over that field; integral endpoint data yield periods over its ring of integers after inverting primes dividing the level. The associated framed motivic classes generate a Hopf subalgebra under Goncharov's coproduct.

Frequency range 3 (FR3) is being explored for sixth-generation (6G) integrated sensing and communication (ISAC).However, experimental evidence on the feasibility of physiological sensing in this band is limited. This paper presents VitalFR3, an SDR-based frequency-modulated continuous-wave (FMCW) measurement platform that integrates a direct-sampling Ettus USRP X440 with a SignalCraft SC2470 frequency converter. To the best of our knowledge, this is the first calibrated SDRbased FMCW platform evaluated for respiration and cardiac-rate estimation from human measurements across multiple FR3center frequencies. Using a 100 MHz waveform, we operate the platform at six RF center frequencies from 10 to 22.5 GHz.We demonstrate how to characterize and calibrate the completeVitalFR3 transmit and receive path directly from loopback recordings, achieving a magnitude error below 0.061 dB at all six frequencies. We then propose a low-complexity end-to-end processing pipeline for vital sign estimation. This involves the identification of a persistent target-associated response in fast time, respiratory tracking in slow time, followed by cardiac- rate estimation. The system is evaluated across 16 human measurements, achieving a respiratory-rate mean absolute error of 0.758 breaths per minute, and the majority of the cardiac- rate estimates fall within 5 BPM of their reference rates. In a separate breath-hold measurement, the estimated cardiac rate is 84.3 BPM versus approximately 84.5 BPM from the reference. These results establish VitalFR3 as a calibrated and configurable measurement platform for experimental physiological sensing across FR3.

Graph Neural Operators (GNOs) provide flexible surrogate models for learning solution operators of partial differential equations (PDEs). However, standard GNOs typically parameterize the integral kernel with a monolithic neural network and evaluate kernel interactions over graph edges, leading to substantial computational and memory overhead at high resolutions or with large neighborhoods. To address these limitations, we propose Functional Tensor Decomposition Graph Neural Operator (FTD-GNO), a memory-efficient GNO framework that decouples the high-dimensional continuous integral kernel into low-dimensional mode-wise functions. By instantiating the kernel with classical tensor decomposition formats, including CP, Tensor-Train, and Tucker decompositions, FTD-GNO enables algebraic reconstruction of the integral operator without explicitly materializing full edge-wise kernel tensors. This factorized formulation reduces the memory footprint of kernel evaluation and aggregation while retaining the continuous operator-learning structure of GNOs. Theoretical complexity analysis shows that FTD-GNO substantially lowers parameter and activation-memory costs associated with high-dimensional kernel construction. Experiments show lower peak memory than the corresponding unfactorized graph-integral baselines, with shorter recorded training times. Fourier-graph experiments further demonstrate that FTD can improve the efficiency of a graph-integral layer within a hybrid operator and has good scalability.

Skeletal motion is stored as every joint's transform at every frame, yet most of it is implied by the body rather than by what the motion is about. Compression is one way to ask what a motion must still say once the body is known, and a production codec must answer it for any skeleton with a stated error bound. Our earlier codec, CurveCodec, matched the mean error of ACL, the production library of modern game engines, with a learned prior over sparse anchors, but not ACL's worst case, and it counted its payload as floats rather than bits. Here we ask where the redundancy of skeletal motion lies and which part of a codec a learned model should take over. Measurements give three answers. At production precision the largest saving comes from predicting each quantized curve from its own past, the second from choosing per joint, in closed loop through the hierarchy, which samples not to code. On the gaps such an encoder leaves, a nearest-neighbour oracle over millions of training samples is no better than linear interpolation, and no learned in-betweener we tried paid for itself. What a network does learn is the distribution of the residuals the codec must send. CurveCodec 2 codes every sub-track as a curve in the log map, quantized in closed loop and thinned to rate-distortion-selected keys, with residuals entropy-coded under a small learned model whose integer inference is bit-exact across platforms. Two contracts are verified on every decoded clip: ACL's own worst case per joint within a stated tolerance, or ACL's mean error per clip. On a held-out test side of 4,472 clips from 33 datasets, CurveCodec 2 needs 0.37x ACL's bytes at ACL's default precision of 0.01 cm under the worst-case contract and 0.22x at 0.1 cm under the mean contract, decodes on one CPU core, and transfers without retraining to a species absent from training. Project page: https://rubbly.cn/publications/curvecodec/

Large language models (LLMs) receive each user message as plain text, even when it combines text from different sources. For example, a user may paste text into a prompt and keep typing a comment directly below it. We study absorption: a phenomenon where the model treats a trailing user comment as part of the pasted text, returning it inside the edited text. This happens even though the user did not intend the comment to become part of that text. Existing instruction-data separation benchmarks tell the model which text is instruction and which is data, then test whether it obeys that separation. They do not test harmless user speech following an unmarked paste. We introduce SEAM, a controlled benchmark of 300 editing examples. Each example is tested under six matched conditions that vary how the boundary between pasted text and later user speech is expressed. Across 20 models, absorption at a bare newline ranges from 7.7% to 66.7%. Adding a blank line does not significantly reduce absorption in any model, while boundary markers reduce it in 19 of 20 models. Comments that fit the pasted text, such as a code comment typed after code, are absorbed significantly more often in 17 of 20 models. Models often fail to separate pasted material from later user speech, and explicit boundaries reduce but do not remove this failure.

We determine the leading logarithmic asymptotics of the fixed-maturity right tail of the SABR model with $\beta\in(0,1)$ and absorption at zero, for every correlation $\rho\in(-1,1)$. If $P(k)$ is the probability that the terminal forward is at least $f_0e^k$, then $-k^{-2}\ln P(k)\to(1-\beta)^2/(2\nu^2T(1-(\rho\wedge0)^2))$ as $k\to\infty$. For $\rho\ge0$ this is the rate predicted by the unrestricted hyperbolic geometry. For $\rho<0$ it is strictly larger: along the volatility excursion that produces the tail, survival forces the noise orthogonal to volatility to stay above a moving square-root barrier, at an additional cost of the same order $k^2$. Consequently the Black-Scholes implied volatility tends to $\nu\sqrt{1-(\rho\wedge0)^2}/(1-\beta)$: Henry-Labordère's conjectured wing limit $\nu/(1-\beta)$ holds for $\rho\ge0$ and fails for every $\rho<0$. For his second conjecture, whose unrestricted-distance Gaussian estimate does not hold for $\rho<0$, we also identify the correct replacement for this model: at the level of tail probabilities, the rate is given by the squared intrinsic Riemannian distance, within the survival domain, from the initial state to the terminal target set. The proofs are direct, combining a stopped Lamperti transform, a conditional time change, Gaussian moving-barrier bounds and change-of-measure constructions, and use no heat-kernel estimates.

We study the slow motion of phase transition layers for a time-fractional Allen–Cahn equation with a Caputo time derivative of order $\alpha\in(0,1)$. We show that the fractional memory preserves the distinction between exponentially and algebraically slow dynamics associated with non-degenerate and degenerate potentials, respectively. In the non-degenerate case, layered solutions persist on an exponentially long time scale of order $\exp(A/(\alpha\varepsilon))$, $A>0$, while in the degenerate case the corresponding algebraic time scale is modified by the factor $1/\alpha$. Finally, we extend the analysis to nonlinear diffusion operators, considering both the $p$-Laplacian and a Perona–Malik type diffusion, showing that the same fractional slow-motion mechanism persists in these more general settings.

Decentralized Gaussian process (GP) methods provide a scalable framework for multi-agent scalar-field estimation by allowing each agent to maintain a local GP over its assigned subdomain. Because neighboring agents condition their GP models on different measurements, their GP posteriors generally disagree over overlapping regions. This paper introduces the inducing points decentralized Gaussian process (IPD-GP) framework, which exploits these discrepancies to improve posterior consistency over shared regions. Each sender constructs receiver-specific data packets by selecting inducing locations targeted at the pairwise overlap and transmitting the corresponding posterior means and variances. Each receiver then selectively assimilates informative packets as persistent fictitious measurements in its local GP. The developed architecture preserves decentralized computation and communication without requiring full dataset exchange or centralized inference. Performance is evaluated using normalized root-mean-square error, negative log predictive density, and their overlap-restricted counterparts, with comparisons against non-communicating local GPs, decentralized aggregation methods, and a centralized GP. Simulation results show that IPD-GP achieves competitive predictive accuracy while reducing inter-agent communication.

Spatial intelligence is a fundamental skill in multiple domains, such as Science, Technology, Engineering, and Mathematics (STEM), Medicine, Architecture, and Construction. Recent studies indicate that Vision-Language Models (VLMs) still face limitations in spatial reasoning, which inhibits artificial intelligence (AI) from performing practical spatial tasks. Using multiple object-rotation datasets developed for training and evaluation, our experiments demonstrated promising improvements in both 2D and 3D rotation detection. Fine-tuned Google DeepMind-built Gemma-4 mixture-of-experts (MoE) models significantly outperformed fine-tuned Gemma-4 generalist models in predicting rotations defined by both their axes and angles. Fine-tuning also substantially improved angle estimation for 2D representation without requiring an explicit coordinate system. Furthermore, identifiable objects did not improve angle-detection accuracy; instead, objects with prominent linear features showed improved performance.

Narrow linewidth (high-Q) quantum discriminators are essential for realizing solid-state $^{229}$Th nuclear clocks, yet the observed transition linewidths remain at the tens-to-hundreds-of-kilohertz level, far exceeding the sub-Hertz linewidth set by the radiative lifetime of the nuclear isomer. Here, we investigate the origin of this broadening in $^{229}$Th:CaF$_2$ through systematic measurements of the linewidth as functions of temperature, thorium concentration, and quadrupole state, accompanied by theoretical analysis and first-principle simulations. We find that the linewidth is independent of temperature, increases linearly with thorium concentration, and depends strongly on the quadrupole state. Data analysis identifies variations of the local electric-field gradient (EFG) as the dominant source of inhomogeneous broadening and reveals that the EFG disorder increases linearly with thorium concentration. The observed Lorentzian line shapes and linewidth linear concentration dependence are explained naturally from the $1/r^3$ scaling of a random distribution of long-range dopant-induced perturbations. Complementary atomistic and ab initio density-functional-theory calculations reproduce these characteristic features and provide insights into the microscopic defect configurations responsible for the broadening. These results establish the dominant broadening mechanism in solid-state $^{229}$Th and provide guidance for engineering nuclear-clock materials with reduced inhomogeneous broadening.