Papers

The Canadian Hydrogen Intensity Mapping Experiment/Fast Radio Burst (CHIME/FRB) instrument is a transient astrophysical burst survey that is discovering FRBs, pulsars, and long-period transients. As a transit telescope, the survey is most sensitive within 2 degrees of the meridian; however, CHIME/FRB can detect bright astrophysical bursts out to its horizon, at 10^-2 to 10^-3 of its peak sensitivity. In this study, we detail the flux density calibration procedure for these bursts detected in the CHIME sidelobes for both channelized voltage (baseband) and intensity data. We validate and estimate the calibration uncertainties by beamforming baseband data towards bright, steady sources in the sidelobes, comparing baseband and intensity flux density calibrations of the same astrophysical transients, and calibrating intensity flux densities for transiting steady sources. We are able to calibrate flux densities for declinations spanning -12 degrees to +59 degrees out to hour angles of 30 degrees, and out to 90 degrees in hour angle for declinations near that of Taurus A (Crab Nebula, declination of about +22 degrees). We conclude that uncertainties in the flux density calibration for transients in the CHIME sidelobes range from 20% to 42%, depending on the data used and the hour angle of the burst.

Behavioral tasks measuring facial affect perception assume that identical stimuli impose equivalent perceptual difficulty across participants. However, this assumption is systematically violated by individual differences in perceptual sensitivity. Using an affective perception task as our testbed, we propose a framework to normalize for perceptual difficulty that directly estimates each participant's Just Noticeable Difference (JND) along the facial affect spectrum via cognitively lightweight perceptual adjustment queries (PAQs). We use these PAQ-inferred JNDs to re-express stimulus distances, constructing difficulty-equated tasks in perceptual space. We validate the framework in a Two-Alternative Forced-Choice (2AFC) task using two complementary behavioral measures: binary metacognitive difficulty judgments and response time variance decomposition. We find that PAQ calibration significantly equalizes perceived task difficulty at an individual level when compared to both the non-calibrated baseline and population-level Weibull calibration, while also reducing mean response time and between-subject variance in response time. These results establish PAQ as a principled and practical instrument for individualized perceptual calibration in facial affect recognition.

Molecular gas plays a central role in regulating star formation and galaxy evolution, yet observational constraints at cosmic noon remain biased toward massive, metal-rich systems. We present ALMA Band 3 observations of the CO J=3-2 transition in 26 unlensed star-forming galaxies from the ALMA Chemical Evolution (ACE) Large Program at z~2-2.5, probing stellar masses of $10^{9} < M_\star < 10^{10.5}\,\mathrm{M}_{\odot}$ and sub-solar metallicities (8.2 < 12 + log(O/H) < 8.6). We derived molecular gas masses using a metallicity-dependent CO-to-H$_2$ conversion factor and alongside analysed stacking measurements and a homogenized literature compilation spanning both local and high-redshift galaxies. We find that the ACE galaxies extend established molecular-gas scaling relations to an order of magnitude lower stellar masses than previously explored at cosmic noon. The molecular gas mass ($M_{\rm mol}$) correlates tightly with star formation rate (SFR), while molecular gas fractions show a strong dependence on specific star formation rate (sSFR) and offset from the star-forming main sequence. In contrast, molecular gas fractions show only weak trends with stellar mass and no significant dependence on metallicity. Molecular gas depletion times are ~1 Gyr and vary little with stellar mass or metallicity, and weakly with sSFR and offset from the star-forming main sequence. Together this further reinforces that the availability of molecular gas is the primary driver of the SFR in galaxies, with changes in star-formation efficiency playing a secondary role. Leveraging the expanded parameter space probed by the ACE and literature samples, we derive a new empirical prescription for predicting $M_{\rm mol}$ as a function of SFR and sSFR. The persistence of the observed scaling relations suggests a largely universal framework governing the molecular gas-star formation cycle across cosmic time.

We use the series representation of the Bessel functions of type $B_N$ in terms of Jack polynomials and show that $$\lim_{k_1\to\infty} J_{(k_1,k_2)}^B(x,k_1y)^{1/k_1}= 2^N\prod\limits_{i=1}^N \Bigg( e^{\sqrt{1+x_i^2 y_i^2}-1}\cdot \frac{1}{\sqrt{1+x_i^2 y_i^2}+1} \Bigg)$$ for $x,y\in\mathbb R^N$ and $k_2\ge0$. Moreover, the known Laplace-type integral representations for $N\ge1$ and $k_2=0,1/2,1,2$ and for $N=2$ and $k_2>0$ by Rösler and Demni respectively lead to related limits for $$\lim_{k_1 \to \infty} \partial_{x_j} J_{(k_1,k_2)}^B(x,k_1y) /(k_1 \cdot J_{(k_1,k_2)}^B(x,k_1 y)) \quad (j=1,\ldots,N).$$ These limits lead to weak limit results for the associated Bessel processes with drift. For $k_2=1/2,1,2$, these limit results have applications to radial parts of Brownian motions with drift on the $M\times N$-dimensional matrices over $\mathbb R,\mathbb C$, and the quaternions for $M\to\infty$. We also discuss these limits in the Dunkl case $N=1$.

This paper proposes structured channel-parameter estimators for reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) systems employing uniform rectangular arrays under line-of-sight propagation. By exploiting the Kronecker and multilinear structures of the cascaded channel, we introduce the Successive Kronecker Factorization (SKF) alongside two Third-Order Tensor Parameter Estimation (TOPE) methods: TOPE-ALS and TOPE-HOSVD. These estimators recover spatial signatures from the pilot-filtered signal matrix, and then decouple the corresponding horizontal and vertical spatial frequencies. This structured formulation achieves benchmark estimation accuracy while reducing computational complexity, offering a efficient solution for RIS-aided systems.

We prove sharp $L^{4}$ Strichartz estimates for two-dimensional periodic Schrödinger flows with integral diagonal symbols $ak_{1}^2+bk_2^2$ where $a,b \in \mathbb Z \setminus \{0\}$. The estimates exhibit a sharp arithmetic dichotomy according to whether $-ab$ is a square: for frequencies bounded by $N$, the optimal loss is $(\log N)^{1/4}$ when $-ab$ is not a square and $N^{1/4}$ when $-ab$ is a square. As a consequence, we show that arbitrarily small perturbations of the rectangular aspect ratio can lead to a transition between global well-posedness and norm inflation for cubic hyperbolic NLS.

In this paper, we shall use the $L^2$ existence theorems for $\partial\bar{\partial}$ provide by Guy Laville to etablish for existence theorem for the $\partial\bar{\partial}$-Neumann operator on any bounded pseudoconvex starred domaine $\Omega$ in $\mathbb{C}^n$ based on the work of D. Spencer on the $\bar{\partial}$-Neumann. As a result, we obtain a new method for resolving the $\partial\bar{\partial}. $

We prove that every finite Helly complex is isomorphic, at the level of its $1$-skeleton, to the Hellyfication (equivalently, the discrete injective hull) of its combinatorial boundary equipped with the metric induced from the complex. In particular, the boundary-rigidity phenomenon for Helly complexes proved by Blufstein-Chalopin-Chepoi admits a canonical injective-hull interpretation, independent of reconstruction procedures based on dismantling.

Sliding friction lowers the jamming packing fraction of dense suspensions and, when activated by stress, drives non-inertial shear thickening. Additional rolling resistance lowers the jamming packing fraction further and can represent effects of particle roughness or angularity. How it changes particle motion on the approach to jamming remains unclear. Using stress-controlled two-dimensional discrete-element simulations, we compare a sliding-only suspension with systems having either uniform or surface-varying rolling friction. At fixed packing fraction, adding rolling friction changes continuous shear thickening into discontinuous shear thickening. At the same distance from the stress-dependent jamming point, $\Delta\phi=\phi-\phi_m(\sigma)$, however, the flow curves nearly collapse, showing that the rheological effect arises largely from the shift in $\phi_m$. Guided by this collapse, we compare particle kinematics in the high-stress thickened state at matched $\Delta\phi$, revealing differences hidden by the similar bulk response. Translational velocity correlations extend over several particle diameters, whereas rotational correlations remain local. Rolling friction promotes co-rotation at contact in place of strong counter-rotation and suppresses rotational relative to translational fluctuations. Rotation nevertheless becomes increasingly important near jamming in every case. The suspension with surface-varying rolling friction follows the behavior of a uniform system with $\mu_r\approx0.3$ because the coefficients sampled at contacts lie well below the surface average value, here $\mu_r\approx0.5$. Thus, $\Delta\phi$ largely organizes the shear-thickening rheology, but not the particle kinematics. These retain a distinct signature of the rolling constraint that must be considered when rolling friction is used to model rough or angular particles.

Complex metallic alloys exhibit rich disorder-driven electronic, magnetic, and vibrational behavior arising from strong chemical disorder, leading to unconventional structure-property relationships with applications in extreme-environment materials, catalysis, spintronics, and thermoelectrics. Despite their technological relevance, the microscopic nature of charge redistribution and electrostatic fluctuations in chemically disordered alloys remains incompletely understood. Here, we develop a theoretical framework that uncovers universal statistical trends of disorder-driven charge transfer and Madelung-field fluctuations. Our analytical formalism demonstrates that local charge transfer and electrostatic potentials exhibit Gaussian-like statistics and universal linear charge-potential (qV) correlations emerging directly from the underlying disorder landscape. We identify the physical origin of these correlations in the interplay between electronic screening and impurity scattering and show how their statistical properties depend on carrier density, disorder strength, and compositional complexity. We further derive scaling relations governing qV trends across binary and multicomponent alloys, including high-entropy materials. Large-supercell density-functional theory (DFT) calculations show good quantitative agreement with the predicted statistical behavior for representative metallic alloys. Our results provide a computationally efficient framework for incorporating disorder-driven electrostatic fluctuations into effective-medium electronic-structure theories and establish a statistical-physics foundation for the predictive design of complex alloys.

In strategic interactions, deterrence is an outcome where one party incentivizes the other party to not participate. This concept can be applied to Colonel Blotto games between two generals where troops can be deterred from following orders by the actions of the opposing general. In this setting, deterrence depends not only on how generals allocate troops, but also on the information available to troops when they decide whether to follow orders or defect. In this work, we study a two-battlefield Colonel Blotto model of deterrence under multiple information structures, ranging from decisions made with only aggregate information to decisions made after local battlefield conditions are observed. We show how different information structures alter the structure of the induced game, affect the existence of equilibria, and substantially change expected utilities. Our findings also prove that the ratio of troops available to each general combined with a capture probability threshold is enough to inform generals about what information they want their troops to have access to.

The Birnbaum-Saunders (BS) distribution has become a widely used model for positive and asymmetric continuous data. Several extensions of the BS distribution have been proposed, including regression formulations that relate its parameters to covariates. In this paper, we introduce a new regression model for the Generalized Birnbaum-Saunders (GBS) distribution, an extension that has received limited attention in the literature despite offering a stronger physical interpretation. The proposed framework follows the structure of Generalized Additive Models for Location, Scale, and Shape (GAMLSS), allowing covariate effects to be incorporated into all three parameters of the distribution, thereby providing greater flexibility for modeling data. In particular, one of the model parameters has a direct interpretation as the median of the response variable, facilitating the interpretation of covariate effects on the conditional median. Parameter estimation is performed via maximum likelihood, and hypothesis tests are proposed based on the Wald test. The proposed regression model is implemented in R through the gamlss package, allowing access to a broad range of tools for model fitting, diagnostics, and assessment. Monte Carlo simulation studies are conducted to investigate the finite-sample performance of the maximum likelihood estimators. The results show that the estimators exhibit desirable properties, with bias decreasing and efficiency increasing as sample size grows. Additionally, the behavior of the Wald test is investigated, showing good performance for moderate to large sample sizes. Finally, two applications to real data illustrate the practical usefulness of the proposed GBS regression model, demonstrating that it is a flexible alternative for modeling positive and asymmetric data compared to the BS model

Accurate channel modeling and estimation of active reconfigurable intelligent surface (RIS)-assisted links with densely integrated elements are essential to fully unleashing this technology's potential. This work adopts a physically consistent model incorporating mutual coupling (MC) effects, modeled via scattering parameters, in RIS-aided communication. We formulate the MC-aware channel estimation as a compressed sensing (CS) problem. The MC effect leads to an increase in the sensing matrix dimensions. This increased dimensionality substantially elevates the complexity of the formulated CS problem. To overcome this, we propose a low-complexity estimator that leverages the structure of the scattering matrix and MC mechanisms to obtain a reduced-size design sensing matrix. Numerical results demonstrate that our approach outperforms MC-unaware estimators by several dBs, achieving accuracy comparable to fully MC-aware solutions but with significantly lower complexity.

Automatic target recognition (ATR) with synthetic aperture sonar (SAS) supports advanced naval capabilities, but deep learning is constrained by scarce target imagery, background clutter, and human-in-the-loop assessment. We adapt DINOv3 Vision Transformer (ViT) models to underwater SAS ATR using a three-stage parameter-efficient framework. Stage 1 uses Low-Rank Adaptation (LoRA) while freezing the ViT backbone, bridging the gap between natural-image pretraining and underwater acoustic propagation. Stage 2 uses hard-negative mining to strengthen the decision boundary against acoustic mimics, including rocks and sediment formations resembling man-made targets. Stage 3 uses Supervised Contrastive Learning (SupCon) to separate target and clutter representations. We evaluate at-sea SAS data using a mission-level geographic split, compare all arms at 85 percent test recall, and repeat each comparison over three random seeds. LoRA accounts for the primary effect, increasing area under the precision-recall curve (AUPRC) from 0.300 to 0.679 +/- 0.027 using the same frozen backbone. Rank 4 achieves this result while training only 0.26 percent of weights. Neither refinement stage exceeds its matched control: hard-negative mining changes AUPRC by -0.0045 +/- 0.0119 versus an equal-size random curriculum, and SupCon changes AUPRC by +0.0002 +/- 0.0096 versus the preceding stage. These null results indicate that mining occurred on data the encoder had already fit and that supervised stages had already imposed most target-clutter geometry. One efficient adaptation stage is sufficient; stacked refinement is not.

We determine the multiplicative structure on the Tor algebras associated to the coordinate rings of general points in $\mathbb{P}^3$ in terms of the number of points. We show that in codimension four, the Waring rank of a form determines the Tor algebra class of its apolar Artinian Gorenstein ring for a dense subset of the forms of fixed Waring rank and sufficiently large degree.

Plant growth and agricultural production form the foundation of a country's sustainable development and directly impact human livelihoods. Recent advances in frontier artificial intelligence have enabled scientific agriculture with strong potential to improve crop productivity. In this paper, we identify the importance and inherent complexity of plant shade simulation, as shading is a critical factor influencing plant growth. To advance this field and promote broader societal benefits, we focus on two main contributions. First, we introduce a comprehensive plant growth and shade dataset covering four plant species, including soybean, tomato, sugarbeet, and strawberry. The dataset includes top-down viewpoints with a supplementary light along a circular trajectory, casting dynamic shadows across multiple growth stages and diverse observation complexities. Second, we propose generative shade simulation based on diffusion models, enabling realistic shade generation for unseen plants and supporting downstream robotic tasks such as perception, lighting control, and view planning. The model incorporates temporal conditioning to facilitate flexible shade simulation across different time stages. We conduct both quantitative and qualitative evaluations to assess model performance. This work provides a foundational study for plant-aware shade modeling and has meaningful implications for broader agricultural and robotic applications.

Language models can now write GPU kernels that outperform PyTorch. We evaluate five model configurations on KernelBench level 1 and find that a frontier model produces correct kernels for 91.1% of problems and independently verified speedups on 22 of 56, including three convolutions, with a median of 1.235x. Open-weights models are far behind: the best reaches 30.4% correct with three verified speedups and solves zero convolutions. We then ask a question the literature does not: what fraction of a real model's wall clock do such kernels govern? Profiling seven workloads across three domains, we find the addressable fraction ranges from 8.9% to 58.2%. On transformers, 80-86% of runtime is spent in cuBLAS GEMM and FlashAttention, bounding realistic end-to-end improvement at roughly 1%, and the fraction shrinks with model scale. On recommenders it is 58.2%, concentrated in a single embedding kernel. We introduce DLRM-Bench, 12 recommender kernel problems in KernelBench format, and measure a 41.7% win rate at a 1.552x median there, projecting 8.63% end-to-end. Separately, we show that KernelBench's correctness check (torch.allclose with an absolute tolerance) is satisfied by a tensor of zeros on 4 of 60 level-1 problems. Two kernels in our own results exploited this before we detected them, including one scored at 283x that wrote 0.3% of its output buffer. We propose scale-invariant replacements and release all 879 evaluations.

Federated learning (FL) enables collaborative model training without sharing raw data, but its performance degrades under non-IID data and stochastic client participation. Remedies built on classical Federated Averaging (FedAvg) typically presuppose that client participation probabilities are known to the server, which is rarely the case in deployed systems. We first discuss and then characterize the optimization problem that distributionally agnostic FedAvg actually solves when participation is entirely unknown, possibly highly skewed, and of variable size across rounds: uniform aggregation is shown to minimize a well-defined stochastic objective, weighted by the participation-induced marginal, at a standard $\mathcal{O}(1/\sqrt{T})$ rate for convex and possibly nonsmooth losses. Building on this characterization, we propose Federated Risk-Averse Averaging (FedeRage), a risk-averse extension of FedAvg that embeds the Conditional Value-at-Risk (CVaR) into the local objective within a natural distributionally robust optimization (DRO) framework. FedeRage implicitly upweights high-loss and infrequently participating clients while adding only a single scalar per-client, and admits an $\mathcal{O}(\kappa/\sqrt{T})$ rate in which the factor $\kappa$ is the upper bound on the “price" of risk aversion. In contrast with aggregation-alignment schemes based on optimal transport, which require the availability distribution as an input, FedeRage remains agnostic to it. Several experiments on three heterogeneous benchmarks indicate consistent improvements over state-of-the-art methods in accuracy, fairness, and convergence speed.

This paper develops a Poisson regression model with multivariate sample selection, in which the outcome is observed only when several potentially correlated selection conditions are satisfied. To the best of our knowledge, this is the first Poisson sample selection model that allows for an arbitrary number of selection equations. We derive the conditional mean of the observed outcome under joint normality of the outcome and selection errors and obtain a multivariate selection-correction term. We prove identification of the model parameters and show that, under suitable support and rank conditions, the outcome parameters can be identified without an exclusion restriction. We also propose two-step estimation procedures based on nonlinear least squares and Poisson pseudo-maximum likelihood. To the best of our knowledge, this paper is the first to apply PPML to a Poisson regression model with sample selection. The consistency of both estimators is established, and a robust two-step sandwich covariance matrix is proposed to account for the estimation error from the first-step selection model. In addition, factorial moments are used to recover the variance of the latent outcome error and the correlations between the outcome and selection errors. Monte Carlo simulations show that ignoring sample selection leads to persistent bias when the outcome and selection errors are correlated, while the proposed PPML estimator substantially reduces this bias and is more stable than nonlinear least squares, especially under moderate and strong selection dependence.

Signal processing techniques for wireless communications and sensing fundamentally differ between near-field and far-field propagation regimes. Accurately identifying the applicable propagation region is therefore essential for enabling efficient beamforming and channel estimation in ultra-massive MIMO (UM-MIMO) systems. This paper proposes a fully unsupervised learning framework to distinguish near-field from far-field propagation based solely on received signal measurements, before estimating the communication distance, and without relying on channel state information. The proposed approach exploits spatial signal power variations across subarrays of a UM array as a physics-inspired feature extraction stage, followed by the OPTICS clustering algorithm to infer the communication region. Simulation results under various system configurations and signal-to-noise ratio (SNR) levels demonstrate that the proposed method accurately identifies the near-field and far-field regions, showing agreement with theoretical boundaries.

Image diffusion models have shown impressive image generation capabilities but are often hard to control, in contrast to classical computer graphics pipelines such as physically based rendering. However, we observe that there is a bridge between light transport phenomena and the distribution of latent space values produced by such models. Thus, we introduce physically based rendering in the feature space learned by the variational autoencoders in generative models, enabling light transport simulation in the latent space. This allows us to leverage physically based rendering techniques to output latent maps for physically guided content generation. We propose modifications to the rendering equation, which, when paired with a differentiable renderer, can yield an optimal set of scene parameters that require only minimal refinement to accurately render into the pretrained latent space. We train our method on a single rendered image, and then demonstrate the generalization of the method to scene geometry changes, lighting changes, and camera view changes.

The iterative Linear Quadratic Regulator (iLQR) is a widely used algorithm for nonlinear trajectory optimization. At each iteration, it solves a local linear-quadratic approximation of the problem via dynamic programming, propagating a quadratic cost-to-go function. If the Hessian of the cost-to-go approximation is positive-semidefinite, one can derive a square root formulation of iLQR that propagates its Cholesky factor instead. This offers significant numerical advantages - much as square root Kalman filters improve upon their conventional counterparts - particularly when iLQR is used within an augmented Lagrangian framework for handling constraints, where large penalties degrade conditioning. Previous square root formulations of iLQR and related algorithms exist, but they are either numerically suboptimal, algorithmically complex, or both. In this paper, we show that the key to an effective square root formulation lies in the Gauss-Newton (weighted least-squares) structure of the cost function: this yields a positive semidefiniteness property that extends beyond the Hessian to the full augmented cost-to-go matrix, and enables a backward pass of remarkable simplicity in which each step reduces to a single QR-decomposition, from which the feedback gain and propagated Cholesky factor are extracted directly.

Group representations very comfortably admit a higher categorical generalization. This includes induction and restriction for 2-representations that very directly parallel classical definitions. An appropriate character theory for 2-representations has been more opaque. In this paper we draw from a range of motivations to provide an intuitive character theory for 2-representations. It is built from the bicategorical trace developed to describe topological fixed point theory. We use the secondary traces of Ben-Zvi and Nadler which connect to Riemann-Roch and Lefschetz-type theorems in the context of differential graded categories and Fourier-Mukai transforms. Additional sources of motivation include Lipmans' work on Grothendieck duality and, crucially, the Bartlett and Ganter–Kapranov approaches to characters. (The second of these was in turn motivated by Hopkins, Kuhn and Ravenel's work on equivariant Morava $E$-theories.) Our characters are compatible with restriction and induction and, in cases that are sufficiently finite, admit a secondary character.

When computing with univariate polynomials, two fundamental and related problems are the XGCD and rational reconstruction, classically solved in quasi-linear complexity using the half-gcd algorithm. These problems have various applications in algebraic computations and bear strong connections to linearly recurrent sequences, structured matrices, and continued fractions. This article first gives a collection of algorithmic reductions, showing that rational reconstruction and XGCD can be solved via the computation of bases of relations modulo a freely-chosen polynomial $M(x)$. In particular, one recovers the folklore idea that bases of Padé approximants (i.e., $M(x) = x^d$) can be used to perform quasi-linear rational reconstruction or XGCD, extending to fast algorithms the well-known link between the Berlekamp-Massey algorithm and the extended Euclidean algorithm. One highlight of these reductions is that, instead of approximants, one may rely on Cauchy interpolants (i.e., $M(x)$ vanishes at chosen points). In a second part, this article describes divide-and-conquer algorithms for approximants and interpolants along with complexity analyses showing an explicit leading constant in front of the dominant term. For interpolants, the best leading constant is obtained through a variant that stores polynomials represented by evaluations, and exploits fast extrapolation in order to avoid repeated conversions to the monomial basis; this requires special points, in geometric or arithmetic progression, or FFT points when the base field allows them. Combining the analyses with the reductions leads to the best complexity bounds we are aware of for rational reconstruction and XGCD. Perhaps surprisingly, even Padé approximants or Berlekamp-Massey-like computations, which intrinsically involve $M(x) = x^d$, are accelerated by reducing them to Cauchy interpolation at well-chosen points.

Unlike ordinary time, a Stieltjes clock may advance continuously, remain constant over intervals, or jump. For an ordinary continuous clock, Hölder regularity with exponent $\alpha>1$ forces constancy, whereas jumps of a Stieltjes clock may allow nonconstant behavior. We refer to Hölder regularity of exponent $\alpha>1$ measured relative to g as super-g-Hölder regularity, and show that, in finite dimensions, such functions admit an atomic representation determined entirely by their jumps, with their g-Hölder seminorms given exactly by the corresponding normalized jump sizes. This atomic representation yields a linear isometric description of the associated function space, together with its Banach and separability properties, an exact total-variation formula with an optimal bound, and finite-jump approximation results. We then apply this structure to Stieltjes differential equations. Nonzero state jumps require positive clock jumps, leading to quantitative finite-jump bounds and, for affine dynamics, exact thresholds for the number of jumps and extremal terminal distances under a prescribed total Stieltjes mass. Finally, we study recovery of the Stieltjes clock from observed state jumps. For known single-valued dynamics, clock jumps can be recovered under a natural local identifiability condition, while for nonconvex differential inclusions the super-g-Hölder bound can reduce, and in some cases remove, nonuniqueness.

We characterize, up to universal constants, the total variation distance between finite products of arbitrary probability measures by a simple formula. A theorem of Latala reduces this expression to one scalar equation. As an application, we characterize the sample complexity of equal-prior binary hypothesis testing uniformly in the weak-detection regime, where squared Hellinger distance alone does not determine the answer, and also characterize the TV distance between multinomial distributions.

In this article, we study unique continuation properties at infinity for solutions to generalized Schrödinger equations with potential functions that belong to the reverse Hölder class. For equations of the form $-div (A \nabla u) + V u = 0$ in $\mathbb{R}^n$, where $A$ is bounded and elliptic and $V \in RH_p$ for some $p \in [\frac n 2, \infty]$, we prove that if a solution doesn't grow too quickly at infinity, then it must be trivial. We use $d_V$, the Agmon distance function associated to $V$, to quantify the threshold growth rate. More precisely, there exists a constant $\gamma_0 > 0$ so that if $|u(x)| \lesssim \exp(\gamma d_V(x, 0))$ for some $\gamma < \gamma_0$ and every $x \in \mathbb{R}^n$, then $u$ must be trivial. The result may be interpreted as a Liouville-type theorem and is related to Landis' conjecture. Our proof techniques are inspired by Z. Shen's exponential decay estimates for fundamental solutions of Schrödinger operators and involve the application of a Fefferman-Phong inequality.

Given a noncomputable, computably enumerable set $D$, we construct a computable structure $G$ such that any two computable copies of $G$ are computably isomorphic while there are two $D$-computable copies of $G$ that are not $D$-computably isomorphic. In other words, $G$ is computably categorical, but not computably categorical relative to $D$. Conversely, we construct a computable structure that is not computably categorical, but is computably categorical relative to $D$. These results differ from those in the literature regarding computable categoricity and its relativiziations because the degree $D$ is given instead of constructed. Our work negatively answers a question of Downey, Harrison-Trainor and Melnikov in the computably enumerable case.

Choreographed aquatic performances require small autonomous surface vehicles to track precise paths under per-thruster force and rate limits, including after thruster failures. We report a deployed system in which trajectory tracking, thrust allocation, and the per-thruster force and rate limits are resolved in a single quadratic program over the per-thruster commands, with fault reconfiguration entering through one binary flag per thruster from an external detector. The system has driven a fleet in live performances on Lake Zürich and at the Time Space Existence 2025 exhibition in Venice. The field campaign measures 1.6 cm root mean square position error in a 10-minute hold and 4.3 cm over a 10 m square at 0.6 m/s. At 0.5 m/s, losing the front thruster increases the error to 11.6 cm, while losing the starboard-side thruster increases it to 11.5 cm. Losing two thrusters simultaneously leaves the craft tracking a 0.4 m/s square with a root mean square position error of 1.25 m. Compared to our own cascaded baseline, the unified formulation tracks the nominal square to the same few centimeters and holds station more tightly with roughly half the thruster force. The architectures separate after a thruster failure, where the unified controller stays within 24 cm of the reference path while the cascade leaves it.

Collecting real-world robot data for dexterous manipulation is costly and time-consuming. While high-fidelity physics simulators enable scalable data synthesis and policy learning, constructing deployment-ready digital twins manually remains labor-intensive, and residual visual, geometric, and dynamics gaps hinder reliable sim-to-real transfer. We present DEXTERA, an automated real-to-sim-to-real framework that transforms a single RGB image into deployable policies for dexterous manipulation across four unified stages: (1) single-image scene factorization into a static Gaussian background and interactive rigid or articulated assets with VLM-inferred physical parameters; (2) metric scene global alignment, object canonicalization, and morphology-balanced robot calibration; (3) scalable simulator task primitive construction, VR teleoperation, and object-centric trajectory synthesis; and (4) a shared multimodal policy interface supporting both imitation learning and reinforcement learning. We evaluate DEXTERA across 13 task-embodiment pairs, 2 dexterous robot platforms, and 6 policy architectures. Experimental results demonstrate that DEXTERA achieves superior visual fidelity and 3D geometric reconstruction compared to generative baselines, while cross-domain trajectory replays validate strong physical interaction consistency. Furthermore, simulation-only trained policies enable viable zero-shot real-robot deployment, while simulation-real co-training substantially improves mean physical policy success from 29.2% to 61.9% across diverse policy architectures. Project website: https://dextera-project.github.io/