arXiv preprints from January 1, 2026 through September 30, 2026 — 03:28:25 EST
Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin degrees of freedom are encoded in low-lying electronic levels, and interactions among the spins...
We are concerned with the justification of the statement, commonly (explicitly or implicitly) used in quantum scattering theory, that for a free non-relativistic quantum particle with initial wave function $Ψ_0(\boldsymbol{x})$, surrounded by detectors along a sphere of large radius $R$, the probability distribution of the detection...
Recent alignment studies commonly remove introductory boilerplate phrases from supervised fine-tuning (SFT) datasets. This work challenges that assumption. We hypothesize that safety- and reasoning-oriented prefix sentences serve as lightweight alignment signals that can guide model decoding toward safer and more coherent responses....
We relate the uniqueness of asymptotic limits for noncollapsed Ricci flat manifolds with linear volume growth to the existence of a harmonic function asymptotic to a Busemann function. Parallel to the work of Colding--Minicozzi in the Euclidean volume growth setting, we prove uniqueness of the asymptotic limit and establish a...
This paper studies state-dependent local projections (LPs). First, I establish a general characterization of their estimand: under minimal assumptions, state-dependent LPs recover weighted averages of causal effects. This holds for essentially all specifications used in practice. Second, I show that state-dependent LPs and VARs target...
This letter proposes a three-tier computational architecture for the real-time control of nonlinear complex systems, such as time-dependent PDEs. There is an important class of such problems for which existing single- and two-time-scale approaches are fundamentally insufficient due to lack of a priori system knowledge, computational...
Volunteer moderators play a crucial role in sustaining online dialogue, but they often disagree about what should or should not be allowed. In this paper, we study the complexity of content moderation with a focus on disagreements between moderators, which we term the ``gray area'' of moderation. Leveraging 5 years and 4.3 million...
We show that for unconstrained Deep Linear Discriminant Analysis (LDA) classifiers, maximum-likelihood training admits pathological solutions in which class means drift together, covariances collapse, and the learned representation becomes almost non-discriminative. Conversely, cross-entropy training yields excellent accuracy but...
Long-horizon robotic manipulation is increasingly important for real-world deployment, requiring spatial disambiguation in complex layouts and temporal resilience under dynamic interaction. However, existing end-to-end and hierarchical Vision-Language-Action (VLA) policies often rely on text-only cues while keeping plan intent latent,...
Magnetic structures, which play a central role in determining their physical properties, are known for only very limited compounds. Traditional theoretical approaches to predicting magnetic structures predominantly rely on first-principles calculations. A key challenge of these methods is their requirement for initial magnetic...
The textile industry in Bangladesh is one of the most energy-intensive sectors, yet its monitoring practices remain largely outdated, resulting in inefficient power usage and high operational costs. To address this, we propose a real-time Non-Intrusive Load Monitoring (NILM)-based framework tailored for industrial applications, with a...
In a recent letter Roca-Maza and Jakubassa-Amundsen claim a large $\approx 5\%$ radiative correction to the parity-violating asymmetry $A_{pv}$ in electron-nucleus scattering. If true, this would be important for the interpretation of the PREX, CREX, and MREX experiments. However, Roca-Maza and Jakubassa-Amundsen do not explicitly...
In gravitational lensing, the Mass-Sheet Transformation (MST)-or mass-sheet degeneracy-leaves image positions unchanged while scaling magnifications and time delays. The transformation scales the lens mass distribution and superposes a uniform mass sheet, but this formulation offers no clear physical interpretation. Here I show that...
Prompt-based methods, which encode medical priors through descriptive text, have been only minimally explored for CT Image Quality Assessment (IQA). While such prompts can embed prior knowledge about diagnostic quality, they often introduce bias by reflecting idealized definitions that may not hold under real-world degradations such...
For simple Lie algebras we construct characteristic identities for split (polarized) Casimir operators in representations $T \otimes Y_n$ and $T \otimes Y_n'$, where $T$ -- defining (minimal fundamental for exceptional Lie algebras) representation, $Y_n$ -- n-Cartan powers of the adjoint representations $ad = Y_1$ and Y_n' -- special...
The atomic response to an ultra-intense driving field produces a characteristic high-harmonic spectrum featuring a rapid drop in intensity for the lower harmonics, followed by a plateau and a sharp cutoff. This response vanishes for circularly polarized classical drivers -- a limitation that can be overcome by introducing quantum...
Using the $\mathbb{R}((X))$-measure, we define and study certain $\mathbb{C}((X))$-valued functions on $\mathrm{GL}_n(F)$ for $F$ a two-dimensional local field. In particular, we define a convolution product on such suitable functions, which leads us to define the Hecke algebra of $\mathrm{GL}_n(F)$. We then define the measurable...
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions, and scientific standards dictate methodological requirements. Applying rules to such inputs...
Diffusion models deliver high quality in image synthesis but remain expensive during training and inference. Recent works have leveraged the inherent redundancy in visual content to make training more affordable by training only on a subset of visual information. While these methods were successful in providing cheaper and more...
We provide an elementary proof that revenue-maximizing mechanisms exist in multi-parameter settings whenever the distribution of valuations has finite expectation.
The $m$=2 member of the monophosphate tungsten bronze family has been considered the only one in the family without an electronic instability at low temperature. In this paper, we report the discovery of a charge density wave phase in this compound, with a transition temperature of 290 K and an incommensurate modulation vector...
Precipitation nowcasting is critically important for meteorological forecasting. Deep learning-based Radar Echo Extrapolation (REE) has become a predominant nowcasting approach, yet it suffers from poor generalization due to its reliance on high-quality local training data and static model parameters, limiting its applicability across...
This paper introduces grangersearch, an R package for performing exhaustive Granger causality searches on multiple time series. The package provides: (1) exhaustive pairwise search across multiple variables, (2) automatic lag order optimization with visualization, (3) tidyverse-compatible syntax with pipe operators and non-standard...
In this manuscript, we establish the global well-posedness for master equations of mean field games of controls, where the interaction is through the joint law of the state and control. Our results are proved under two different conditions: the Lasry-Lions monotonicity and the displacement $λ$-monotonicity, both considered in their...
This paper presents a comprehensive study of matrix Kloosterman sums, including their computational aspects, distributional behavior, and applications in cryptographic analysis. Building on the work of [Zelingher, 2023], we develop algorithms for evaluating these sums via Green's polynomials and establish a general framework for...