arXiv preprints from January 1, 2026 through September 15, 2026 — 17:20:17 EST
The article establishes a rigorous shift operator calculus for stationary time series modeling, addressing a certain gap in the literature. It provides proofs of existence and isometry for the transfer function operators $f(B)$ and $f(T)$ where $B$ is the bilateral shift operator and $T$ is the unilateral shift operator for different...
In this short note, we study the spectrum of prime Serre ideals of global representations for noetherian families. In particular, we prove that the spectrum of prime Serre ideals of finitely generated VI-modules is homeomorphic to N^{*}, the one-point compactification of N, which differs from the Balmer spectrum of derived VI-modules....
In this paper, we introduce chemical functions, a unified framework that models chemical systems as noisy challenge--response primitives, and formalize the associated chemical function infrastructure. Building on the theory of physical functions, we rigorously define robustness, unclonability, and unpredictability for chemical...
We establish a lower bound for the principal $p-$frequency $λ_{1,p}(Ω)$ on a bounded domain $Ω$ in a non-compact Riemannian manifold of dimension $n.$ Under the assumption that the Ricci curvature satisfies $\operatorname{Ric} \geq (n-1)K$ with $K<0,$ we prove that $λ_{1,p}(Ω) > \barλ_{D,K,n}$, where $D$ is the diameter of $Ω$ and...
Spatially-resolved photon counting of a twin beam performed by an iCCD camera allows for versatile tailoring the properties of the beams formed by parts of the original twin beam. Dividing the idler beam of the twin beam into three equally-intense parts and post-selecting by detecting a given number of photocounts in the whole signal...
We study non-linear traces of Choquet type on AF algebras. Building on the characterization of Choquet traces on matrix algebras due to Nagisa--Watatani, we generalize the construction to arbitrary unital AF algebras. We show that there is a one-to-one correspondence between such traces and increasing functions on the dimension scale,...
Code understanding is a foundational capability in software engineering tools and developer workflows. However, most existing systems are designed for English-speaking users interacting via keyboards, which limits accessibility in multilingual and voice-first settings, particularly in regions like India. Voice-based interfaces offer a...
We introduce BallotRank, a ranked preference aggregation method derived from a modified PageRank algorithm. It is a Condorcet-consistent method without damping, and empirical examination of nearly 2,000 ranked choice elections and over 20,000 internet polls confirms that BallotRank always identifies the Condorcet winner at...
The quantum anomalous Hall (QAH) insulator is uniquely characterized by the topological Chern number C. Controlling the Chern number is a key step toward functional topological electronics and enables access to exotic quantum phases beyond the traditional quantum Hall physics. Here, we report a series of QAH insulators in twisted...
Allowing for adversarial contamination and heavy tails, we study testing whether the mean of a high-dimensional random vector equals zero. Because standard max-tests based on sample averages are highly non-robust, we propose a max-test based on quantile-winsorized observations. The test controls asymptotic size under adversarial...
Open-vocabulary keyword spotting (KWS) with text-based enrollment has emerged as a flexible alternative to fixed-phrase triggers. Prior utterance-level matching methods, from an embedding-learning standpoint, learn embeddings at a single fixed dimensionality. We depart from this design and propose Matryoshka Audio-Text Embeddings...
The processes of simultaneous coagulation and Ostwald ripening of particles in the concluding stage of phase transformation are considered. We solve the integro-differential system of Smoluchowski-type kinetic and mass balance equations using a computationally efficient numerical algorithm based on low-rank matrices. We compare our...
We investigate the frame dependence of distribution functions within the framework of generalized chiral kinetic theory. Based on the derived transformation rules governing the choice of frame, we analytically obtain the global equilibrium solution in the presence of vorticity and electromagnetic fields. Our results show that, under...
These lectures at Winter School on Intense Laser Science (WiSILS-2024) at IIT Jodhpur, India, will focus on the Relativistic charge particle dynamics in ultra-intense laser pulses. We will be learning about the relativistic equations of motion, Radiation-Reaction, Thomson scattering, Ponderomotive scattering, and its usage as the...
The shift to disaggregated 5G architectures introduces unprecedented flexibility but also significant complexity in Beyond 5G Radio Access Networks (RANs). Open RAN enables programmability through xApps, yet deploying and validating these applications is critical given the nature of the systems they aim to control. Current Open RAN...
We study a cosmological scenario featuring an early phase of null energy condition (NEC) violation. Within this framework, we show that perturbative unitarity bounds place strong constraints on both the amplitude and the spectral tilt of primordial gravitational waves. Our analysis is largely insensitive to the detailed realization of...
Do large language models (LLMs) genuinely understand abstract concepts, or merely manipulate them as statistical patterns? We introduce an abstraction-grounding framework that decomposes conceptual understanding into three capacities: interpretation of abstract concepts (Abstract-Abstract, A-A), grounding of abstractions in concrete...
Let $X$ be a smooth projective curve over a finite field of characteristic $p$. We describe and implement a practical algorithm for computing the $p$-divisible group $Jac(X)[p^\infty]$ via computing its Dieudonné module, or equivalently computing the Frobenius and Verschiebung operators on the first crystalline cohomology of $X$. We...
We develop a mathematical framework to optimize leveraged staking ("loopy") strategies in Decentralized Finance (DeFi), in which a staked asset is supplied as collateral, the underlying is borrowed and re-staked, and the loop can be repeated across multiple lending markets. Exploiting the fact that DeFi borrow rates are deterministic...
Mechanistic Interpretability (MI) has emerged as a vital approach to demystify the opaque decision-making of Large Language Models (LLMs). However, existing reviews primarily treat MI as an observational science, summarizing analytical insights while lacking a systematic framework for actionable intervention. To bridge this gap, we...
Contact electrification give rise to charge accumulation at the interface when two materials are brought into contact with each other. The charge accumulation at the interface will diffuse to the interior of the conducting material if the dimensions of the contacting conducting material is of the order of an unknown critical length...
Community-based fact-checking systems, such as Community Notes on X (formerly Twitter), aim to mitigate online misinformation by surfacing annotations judged helpful by contributors with diverse viewpoints. While prior work has shown that the platform's bridging-based algorithm effectively selects helpful notes at the time of display,...
Query formulation from internal information needs remains fundamentally challenging across all Information Retrieval paradigms due to cognitive complexity and physical impairments. Brain Passage Retrieval (BPR) addresses this by directly mapping EEG signals to passage representations without intermediate text translation. However,...
Unsupervised skill discovery aims to acquire behavior primitives that improve exploration and accelerate downstream task learning. However, existing approaches often ignore the geometric symmetries of physical environments, leading to redundant behaviors and sample inefficiency. To address this, we introduce Group-Invariant Skill...
Short-utterance speaker verification remains challenging due to limited speaker-discriminative cues in short speech segments. While existing methods focus on enhancing speaker encoders, the embedding learning strategy still forces a single fixed-dimensional representation reused for utterances of any length, leaving capacity...