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arxiv.org/abs/1512.08946v2
In this monograph, we lay some foundations of a theory of infinite dimensional Euclidean lattices - and more generally, of infinite dimensional Hermitian vector bundles over some "arithmetic curve" ${\rm Spec}\,\mathcal{O}_K$ attached to the ring of...
arxiv.org/abs/2510.10247v1
Given a submanifold $M\subset \mathbf{R}^ν$, a curve $γ:I\to M$ and tangent vectors $v$ along $γ$, we roll the tangent space along $γ$. In doing so, we get an imprint of $γ$ on the tangent space, as well as an imprint of tangent vectors. We show...
arxiv.org/abs/1302.6207v1
Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for find...
arxiv.org/abs/gr-qc/0301059v3
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely ge...
arxiv.org/abs/2003.12972v1
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\toδ$) drawn from a Gaussian mixture...
arxiv.org/abs/2104.11358v1
During the last two decades, locally stationary processes have been widely studied in the time series literature. In this paper we consider the locally-stationary vector-auto-regression model of order one, or LS-VAR(1), and estimate its parameters by...
arxiv.org/abs/quant-ph/9412006v1
A Kochen-Specker contradiction is produced with 36 vectors in a real 8-dimensional Hilbert space. These vectors can be combined into 30 distinct projection operators (14 of rank 2, and 16 of rank 1). A state-specific variant of this contradiction r...
arxiv.org/abs/2512.06667v1
Our study on nondegenerate dark-bright-bright solitons in a three-component Manakov model with repulsive interactions reveals the existence of diverse branches of nondegenerate vector solitons. For fixed bright component particle numbers and a given...
arxiv.org/abs/1706.08747v3
We define two algebra automorphisms $T_0$ and $T_1$ of the $q$-Onsager algebra $B_c$, which provide an analog of G. Lusztig's braid group action for quantum groups. These automorphisms are used to define root vectors which give rise to a PBW basis fo...
arxiv.org/abs/1410.7646v2
We extend results of Bénéteau, Condori, Liaw, Seco, and the author concerning cyclic vectors in Dirichlet-type spaces to the setting of the unit ball, identifying some classes of cyclic and non-cyclic functions, and noting the necessity of certain...
arxiv.org/abs/2106.03961v1
A search for singly produced vector-like $T/Y$ quark is performed in proton-proton collision data at a centre-of-mass energy of $13$ TeV corresponding to an integrated luminosity of $139.1 fb^{-1}$, recorded with the ATLAS detector at the LHC from 20...
github.com/Vectorized/solady
Optimized Solidity snippets. (⭐ 3280)
arxiv.org/abs/1705.07437v1
A set $S\subseteq\{0,1\}^E$ of binary vectors, with positions indexed by $E$, is said to be a \textit{powerful code} if, for all $X\subseteq E$, the number of vectors in $S$ that are zero in the positions indexed by $X$ is a power of 2. By treating b...
arxiv.org/abs/2505.17810v1
Approximate nearest neighbor (ANN) search is a performance-critical component of many machine learning pipelines. Rigorous benchmarking is essential for evaluating the performance of vector indexes for ANN search. However, the datasets of the existin...
arxiv.org/abs/nlin/0406006v1
Time dependent mode structure for the Lyapunov vectors associated with the stepwise structure of the Lyapunov spectra and its relation to the momentum auto-correlation function are discussed in quasi-one-dimensional many-hard-disk systems. We demon...
arxiv.org/abs/2508.16354v2
In this paper we show an abundance of complete Kähler metrics with negative holomorphic bisectional curvature on total spaces of certain vector bundles. Assume that such total spaces are endowed with a wider class of nonpositively curved Kähler met...
arxiv.org/abs/2411.03965v1
This study explores a Bayesian algorithmic approach to personalized fragrance recommendation by integrating hierarchical Relevance Vector Machines (RVM) and Jungian personality archetypes. The paper proposes a structured model that links individual s...
arxiv.org/abs/2401.11246v1
We propose a natural language prompt-based retrieval augmented generation (Prompt-RAG), a novel approach to enhance the performance of generative large language models (LLMs) in niche domains. Conventional RAG methods mostly require vector embeddings...
arxiv.org/abs/2002.04726v2
We consider a variant of the classical online linear optimization problem in which at every step, the online player receives a "hint" vector before choosing the action for that round. Rather surprisingly, it was shown that if the hint vector is guara...
