arXiv preprints from January 1, 2026 through July 20, 2026 — 01:13:29 EST
Non-axisymmetric magnetic field coils have been designed to provide efficient error field correction and suppress edge localized modes in SPARC - a compact high-field tokamak that is presently under construction at Commonwealth Fusion Systems. These designs utilize the Generalized Perturbed Equilibrium Code's (GPEC's) representation...
Out-of-distribution (OOD) detection remains a fundamental challenge for deep neural networks, particularly due to overconfident predictions on unseen OOD samples during testing. We reveal a key insight: OOD samples predicted as the same class, or given high probabilities for it, are visually more similar to each other than to the true...
Transformer-based models have shown strong performance in time-series forecasting by leveraging self-attention to model long-range temporal dependencies. However, their effectiveness depends critically on the quality and structure of input representations derived from raw multivariate time-series data, particularly as sequence length...
We investigate the nonlinear formation of plasmoids in 2D low-beta current sheets through the interplay between the Kelvin-Helmholtz instability (KHI) and the lower-hybrid drift instability (LHDI). Using a hybrid kinetic-gyrokinetic model-based Super Simple Vlasov (ssV) code with fully kinetic ions and drift-kinetic electrons, we...
Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective in enhancing LLMs short-context reasoning, but its performance degrades in long-context scenarios that require both precise grounding and robust long-range reasoning. We identify the "almost-there" phenomenon in long-context reasoning, where trajectories are...
Accurate instance-level segmentation of organelles in electron microscopy (EM) is critical for quantitative analysis of subcellular morphology and inter-organelle interactions. However, current benchmarks, based on small, curated datasets, fail to capture the inherent heterogeneity and large spatial context of in-the-wild EM data,...
We present the Koopman-Inspired Learned Observations Extended Kalman Filter (KILO-EKF), which combines a standard EKF prediction step with a correction step based on a Koopman-inspired measurement model learned from data. By lifting measurements into a feature space where they are linear in the state, KILO-EKF enables flexible...
A nonlinear rectangular patch antenna (RPA) is presented in which back-to-back Schottky diodes are embedded at high-field regions to enable passive, bias-free harmonic generation. The self-biased diodes introduce a power-dependent impedance that drives efficient frequency up-conversion and selective third-harmonic radiation. A...
In this paper, we prove optimal $k$-systolic inequalities and characterize the case of equality on closed $n$-dimensional Riemannian manifolds with positive intermediate curvature for $3\leq n\leq 7$. This unifies prior works of Bray-Brendle-Neves \cite{BrayBrenleNevesrigidity} and Chu-Lee-Zhu \cite{chuleezhu_n_systole}, and...
The demand of customized large language models (LLMs) has led to commercial LLMs offering black-box fine-tuning APIs, yet this convenience introduces a critical security loophole: attackers could jailbreak the LLMs by fine-tuning them with malicious data. Though this security issue has recently been exposed, the feasibility of such...
We present a consistent relativistic formulation of Mach principle within a geometric theory of gravitation. In this approach, neither inertia nor free fall is assumed a priori. Instead, the motion of any local system arises from its dynamical interdependence, direct or indirect, with the rest of the Universe. This viewpoint provides...
In this paper we generalize the Weierstrass and Malgrange preparation theorems to the symmetric matrix valued case, proving symmetric preparation of analytic and smooth symmetric systems that vanish of finite order.
We take the first step toward a structure theory that includes both operations of a ring $\mathcal{R}$. More precisely, we prove a series of inverse results for the structure of sets $A\subseteq \mathbf{F}_p$ such that, under certain conditions on integers $r_1, \dots, r_k$, one has $|A^{r_1} + \dots + A^{r_k}| \ll \sqrt[k]{p^{k-1} |A|}$.
In this paper we propose an approach for executing data transformations near- or in-storage on intelligent storage systems. The currently prevailing approach of extracting the data and then transforming it to a target format suffers degraded performance during transformation and causes heavy data movement. Our results show robust...
Triple-negative breast cancer (TNBC) is an aggressive disease with high mortality and limited treatment options, due to its lack of receptors that have targeted therapies available. The tumor microenvironment (TME) plays a critical role in TNBC progression and therapeutic resistance. In this work, we developed a novel mathematical...
We provide a cocycle-level Hirzebruch-Riemann-Roch (HRR) identity for arbitrary complex analytic infinity-prestacks. We view this work as the natural setting for Toledo and Tong's HRR philosophy and technical machinery.
This work extends Favard-type spectral representations for banded matrices $T$ beyond the bounded setting. It assumes that, for every $N\in\mathbb N_0$, there exists a shift $s_N\ge 0$ such that the shifted truncation $A_N:= T^{[N]}+s_N I_{N+1}$ admits a positive bidiagonal factorization (PBF). Allowing $s_N$ to depend on $N$ leads to...
Precision measurements of four neutrino oscillation parameters, $θ_{12}$, $θ_{13}$, $Δm^2_{21}$, and |$Δm^2_{31}$|, face significant interference from a previously overlooked correlated background. Recent findings from the SNO+ and JUNO experiments reveal that cascade decays of $^{214}$Bi-$^{214}$Po in liquid scintillator detectors...
In this paper, we prove that the smallest even sets in ${\rm PG}(n,q)$, i.e. sets that intersect every line in an even number of points, are cylinders with a hyperoval as base. This fits into a more general study of dual projective geometric codes. Let $q$ be a prime power, and define $\mathcal C_k(n,q)^\perp$ as the kernel of the...
We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying spaces of the ``braided" automorphism groups of the associated trees. An intermediate step to...
AI agents are autonomous systems that combine LLMs with external tools to solve complex tasks. While such tools extend capability, improper tool permissions introduce security risks such as indirect prompt injection and tool misuse. We characterize these failures as unbalanced tool-driven agency. Agents may retain unnecessary...
Time series anomaly detection (TSAD) is essential for ensuring the safety and reliability of aerospace software systems. Although large language models (LLMs) provide a promising training-free alternative to unsupervised approaches, their effectiveness in aerospace settings remains under-examined because of complex telemetry,...
Federated learning enables collaborative model training across distributed institutions without centralizing sensitive data; however, ensuring algorithmic fairness across heterogeneous data distributions while preserving privacy remains fundamentally unresolved. This paper introduces CryptoFair-FL, a novel cryptographic framework...
We investigate operator delocalization in disordered one-dimensional spin chains by introducing -- besides the already known operator mass -- a complementary measure of operator complexity: the operator length. Like the operator nonstabilizerness, both these quantities are defined from the expansion of time-evolved operators in the...
We show that for any two sets of reals numbers $A=\{a_1,\dots,a_n\}$ and $B=\{b_1,\dots,b_n\}$, the sums of the form $\sum_{i=1}^n a_i\,b_{π(i)}$ always take on $Ω(n^{3})$ distinct values, as we range over all permutations $π\in S_n$. An important ingredient is a ``supportive'' version of Halász's anticoncentration theorem from...