arXiv preprints from January 1, 2026 through September 5, 2026 — 23:29:42 EST
We consider the conformal loop ensemble (CLE) with the parameter $κ=4$, the critical value at or below which the loops are simple and do not intersect each other or the domain boundary. We show that the loops of a CLE$_4$ uniquely determine a conformally invariant, local, and geodesic metric so that the metric ball growth from the...
We study probabilistic numerical methods for solving nonlinear PDEs from a Bayesian nonparametric perspective. Given noisy evaluations at random collocation points, we place a truncated Gaussian series prior on the unknown solution and establish contraction at the minimax nonparametric rate, up to a logarithmic factor. Our main...
Quantum thermalization explains how an isolated many-body system naturally evolves towards a thermal state, rendering information about the initial conditions inaccessible to local measurements. This is precisely the mechanism utilized in quantum error correction, where information is protected by design through a nonlocal encoding....
In this paper, we consider a class of Riemannian nonsmooth composite expectation optimization problems, which arises in various machine learning, signal processing, and statistics applications. Noting that these problems admit structured minimax reformulations, we propose an efficient algorithm, named stochastic Riemannian alternating...
Probability plays two distinct roles in modern data-analytic practice: (i) as an internally coherent, filtration-relative language for sequential forecasting and, together with a stated loss or utility, decision making; and (ii) as a foundation for empirical claims such as stabilization, calibration, and repeated-sampling validity....
We study the near $L^1$ behavior of the maximally quadratically modulated Hilbert transform \[ \mathcal{C}_2f(x) := \sup_λ \left|\operatorname{p.v.} \int_{\mathbb{R}}f(x-y)e^{2 πi λy^2} \frac{\mathrm{d} y }{y} \right| \] and its lacunary counterpart obtained by restricting $λ$ to $2^{\mathbb{Z}}.$ We prove that if $Φ$ is a Young...
This paper investigates a two player zero-sum stochastic differential game characterized by three distinct regimes, reflecting the regime switching dynamics within the system. We aim to derive an explicit solution for a number of configurations of the switching system by means of the viscosity solutions approach. In particular, we...
We study the SCFT/VOA correspondence for the $(A_2,D_{3n-2})$ Argyres--Douglas theories with $n\geq2$. From the matching of the central charges and the equality of the Schur index with the vacuum supercharacter to all orders, we propose that the associated VOA is the logarithmic doublet algebra $\mathcal A(4n-2)$ of Feigin, Feigin,...
Let \(S\) be a smooth projective complex surface with irregularity \(q=h^{1,0}(S)\) and geometric genus \(g=h^{2,0}(S)\), and let \(S^{[n]}\) denote its Hilbert scheme of \(n\) points. We prove that, for every \(n\ge0\), the sequence \[ \left(h^{p,0}\bigl(S^{[n]}\bigr)\right)_{p=0}^{2n} \] is log-concave if and only if...
Let $p$ be a prime. We prove nontrivial bounds on short sums of Dirichlet characters mod $p$ evaluated at a class of polynomials, not necessarily homogeneous, in $n$ variables and of degree $k$. For large $n$, we further achieve nontrivial bounds for sums over boxes with side-lengths as short as $p^{1/(k-1)+\varepsilon}$, which breaks...
We define the new basis of the Grothendieck group of unipotent representations in an exceptional Weyl group, making more precise and correcting results in previous papers.
We develop a global framework for joint S&P 500 (SPX)-VIX smile calibration across multiple maturities without the conditional-independence restriction induced by Markovian stitching. Exact local and global feasibility are equivalent: every globally feasible law has a block-preserving SPX-Markovization that leaves each monthly...
This paper presents an energy-based controller for a multiagent robotic system designed to achieve and maintain a specific formation while moving on a plane and avoiding collisions between agents. The controller emulates a network of elementary spring-damper modules connecting pairs of agents. This network, with its de-energized...
Room impulse responses (RIRs) characterize the acoustic environment of a room by capturing how sound propagates and decays within an enclosed space. In applications such as immersive audio rendering, accurate acoustic reconstruction often relies on spatially densely sampled RIRs. This consequently gives rise to a large volume of RIR...
What are the transversality conditions for an optimal control problem when the boundary conditions are defined by differential equations? This seemingly bizarre question is motivated by trajectory optimization problems in the $N$-body system. The question, however, is more fundamental and goes beyond problems in astrodynamics to...
Terahertz (THz) wireless interconnects offer high-capacity, low-latency, and energy-efficient rack-to-rack links capable of on-demand connectivity reconfiguration, serving as a promising complement to optical fabrics for communication-intensive distributed AI training datacenters. However, co-optimizing optical and THz resources to...
Despite strong performance on held-out electroencephalography (EEG) data, seizure detectors may fail under real-world acquisition variability, artifacts, and adversarial inputs. We introduce RobustSeiz, an open-source, model-agnostic framework that provides a standardized, reproducible protocol for stress-testing and comparing seizure...
Site-specific training can improve wireless receiver performance without increasing computational complexity. However, real-world results have so far focused on fully trainable neural receivers and single-layer transmissions. We study site-specific finetuning of three receiver architectures: fully trainable neural, model-driven...
We present Alignment-Free Text-Audiobox (Text-AB), a unified framework for high-quality voice dubbing and full-duplex dialogue synthesis. Building on a Diffusion Transformer trained with a flow-matching objective, Text-AB departs from the Audiobox system along three dimensions. First, it operates in a latent diffusion framework using...
Practical separation of single-channel co-frequency signals (SCCFSs) is hindered by the prohibitive computational complexity of benchmark algorithms. To address this issue, we propose a low-complexity separation framework based on sequential detection (SD), in which signal separation is cast as a sequential path search over a...
Automatic speech recognition (ASR) remains challenging for individuals with cleft lip and palate (CLP) because of limited pathological speech data and large variations in speech characteristics across speakers and severity levels. These recognition difficulties can reduce the accessibility of voice-based human-computer interaction,...
Multi-Task semantic communication (SemCom) prioritizes simultaneous execution of multiple tasks over bit-accurate reconstruction in future intelligent networks. In our prior work [1], we introduced the cooperative multi-task SemCom (CMT-SemCom) framework, in which the semantic encoder is divided into a common unit (CU) and multiple...
Automatic tissue segmentation is essential for large-scale analysis of histopathology whole-slide images (WSIs), but accurate pixel-level segmentation remains challenging. Pixel-level annotations are expensive to obtain, models pre-trained on natural images may transfer poorly to histopathology, and pathology foundation models,...
The entangled states of composite quantum systems are well studied. The particle-like nature of these systems also means that, while entangled, they can be physically separated and measurements performed on the separated subsystems. Measurements on the separated subsystems A and B should pertain to vectors in the local Hilbert space...
The LZ experiment has reported a single 248 keV nuclear recoil event in their $2.84$ ton-yr exposure on a xenon target. The absence of lower nuclear recoil events is naturally explained by inelastically scattering dark matter (DM), for which the nuclear recoil energy spectra are shifted upwards from zero. Excitingly, the observed rate...