arXiv preprints from January 1, 2026 through September 21, 2026 — 04:33:53 EST
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...
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions follow-remains largely under explored. In this work, we study proof generation in the context of OWL...
The widespread use of Vision Language Models (VLMs, e.g. CLIP) has raised concerns about their vulnerability to sophisticated and imperceptible adversarial attacks. These attacks could compromise model performance and system security in cross-modal tasks. To address this challenge, three main defense paradigms have been proposed:...
Scientific Artificial Intelligence (AI) applications require models that deliver trustworthy uncertainty estimates while respecting domain constraints. Existing uncertainty quantification methods lack mechanisms to incorporate symbolic scientific knowledge, while neurosymbolic approaches operate deterministically without principled...
Incarceration-diversion treatment programs aim to improve societal reintegration and reduce recidivism, but limited capacity forces policymakers to make prioritization decisions that often rely on risk assessment tools. While predictive, these tools typically treat risk as a static, individual attribute, which overlooks how risk...
We establish new connections between integral curvature bounds and the Euler characteristic of closed Riemannian manifolds through the perspective of Schrödinger-type operators. Central to our approach is the twisted Dirac operator \(\mathcal{D}_θ\), whose index equals \(χ(M)\). Under integral smallness conditions on the negative part...
We investigate scalarization of charged quantum Oppenheimer-Snyder extremal (cqOSe)-black hole in the Einstein-Gauss-Bonnet-scalar theory with a nonlinear electrodynamics term. This black hole is described by quantum parameter $α$ and magnetic charge $P$. It is equivalent to the qOS-extremal black hole whose action is still unknown...
Spatio-temporal reasoning is a remarkable capability of Vision Language Models (VLMs), but the underlying mechanisms of such abilities remain largely opaque. We postulate that visual/geometrical and textual representations of spatial structure must be combined at some point in VLM computations. We search for such confluence, and ask...
Connectivity in connected and autonomous vehicles (CAVs) introduces vulnerability to cyber threats such as false data injection (FDI) attacks, which can compromise system reliability and safety. To ensure resilience, this paper proposes a control framework combining a nonlinear controller with an interval observer for robust state...