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Related Articles from SNS
Asymptotic tensor rank is characterized by polynomials
arXiv:2411.15789v2 Announce Type: replace Abstract: Asymptotic tensor rank is notoriously difficult to determine. Indeed, determining its value for the $2\times 2$ matrix multiplication tensor would determine the matrix multiplication exponent, a long-standing open problem. On the other hand, Strassen's asymptotic rank conjecture makes the bold claim that asymptotic tensor rank equals the largest dimension of the tensor and is thus as easy to compute as matrix rank.
Asymptotically Optimal Sequential Testing with Markovian Data
arXiv:2602.17587v2 Announce Type: replace-cross Abstract: We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic, finite-state Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the alternative corresponds to a disjoint set $Q$. We establish a non-asymptotic instance-dependent lower bound on the expected stopping time of any valid sequential test under the...
Justification and structure- and asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation
arXiv:2606.09299v1 Announce Type: new Abstract: We study a hyperbolic approximation ("hyperbolization") of the Cahn-Hilliard (CH) equation, originally proposed by Dhaouadi, Dumbser, and Gavrilyuk (2025, DOI: 10.1098/rspa.2024.0606) and study its convergence towards the CH model in a relaxation limit both via formal asymptotic expansions and, for a slightly modified approximation, via the relative energy framework. Moreover, we develop energy-stable semidiscretizations of the CH equation and...
Asymptotic Optimality of the High-Dimensional Gaussian Mechanism and Improved Low-Dimensional Mechanisms for Differential Privacy
arXiv:2606.08681v1 Announce Type: new Abstract: The additive noise mechanism is a foundational tool for differential privacy (DP) of $T$-dimensional real-valued vector queries. The Gaussian mechanism, utilizing Gaussian noise, is the mostly widely used such mechanism, due to its simplicity and strong privacy guarantees. In this work, we provide justification for this choice, showing that as the dimension $T\to\infty$, no additive-noise mechanism can asymptotically improve on the Gaussian...
An Adaptive Log-Laguerre Spectral Method for the Radial Dirac Equation: Resolving Asymptotic Decay and Core Singularities in Atomic Calculations
arXiv:2604.11063v2 Announce Type: replace Abstract: The high-precision solution of the radial Dirac equation is fundamental to relativistic quantum chemistry, essential for reliable pseudopotential generation and all-electron electronic structure methods. Capturing both the non-polynomial singularities at the origin and the state-dependent asymptotic decay on semi-infinite domains presents a significant computational challenge. In this work, we propose the Adaptive Log-Laguerre Spectral...
Pitot-Aided Attitude and Air Velocity Estimation with Almost Global Asymptotic Stability Guarantees
Announce Type: replace Abstract: This paper investigates the problem of attitude and air velocity estimation for fixed-wing unmanned aerial vehicles (UAVs) using IMU measurements and at least one Pitot tube measurement, with almost global asymptotic stability (AGAS) guarantees. A cascade observer architecture is developed, in which a Riccati/Kalman-type filter estimates the body-fixed frame air velocity and the vehicle's tilt using IMU data as inputs and Pitot measurements as outputs. Under...
Asymptotic Optimality of Thompson Sampling for Risk-Averse Bandits with Sub-Gaussian Rewards
arXiv:2606.09191v1 Announce Type: new Abstract: We prove that $\rho\text{-}\mathrm{NPTS}_{\mathrm{SG}}$, an anchor-free nonparametric Thompson Sampling algorithm for risk-averse bandits, achieves regret matching the instance-dependent lower bound to leading order in $\log n$, establishing it as asymptotically optimal for any continuous risk functional $\rho$ (CVaR, mean-variance, Sharpe ratio, distortion risk measures, and more) on the class of distributions with bounded density and...
Asymptotic Recovery in Fourier Spectral Methods for the Schr\"odinger Equation with Point Singularities
arXiv:2606.01718v1 Announce Type: new Abstract: This paper studies the Fourier spectral method (FSM) for the Schr\"odinger equation with singular potentials $V \in H^{s}$, where $s > \max\{d/2-2,-1\}$ and $d$ denotes the spatial dimension. This setting includes a broad class of singular potentials, such as the 3D Coulomb potential and the 1D Dirac-delta potential.
Asymptotic behavior of the shear flow reactivity enhancement effect
arXiv:2606.06973v1 Announce Type: new Abstract: Fusion reactivity is enhanced in the vicinity of strongly sheared flow due to the tendency of fast ions near the Gamow peak to travel long distances between collisions, thereby sometimes crossing gradients in the background flow and attaining a velocity boost relative to the thermal background. This ``shear flow reactivity enhancement effect'' (SFRE) allows turbulent kinetic energy on fine spatial scales to contribute to fusion reactivity...
Multiple Quantum Hypothesis Testing: One-Shot Pairwise Bounds and Sharp Asymptotics
arXiv:2606.06246v1 Announce Type: cross Abstract: We consider Bayesian discrimination among multiple quantum states and establish a dimension-free one-shot upper bound on the minimum probability of error in terms of the sum of pairwise errors. This resolves a conjecture of Audenaert and Mosonyi Phys. 55 (2014)] and improves the multiple quantum Chernoff bound of Li