Vector Fields on Product Manifolds [PDF]
arXiv, 2011 This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on ...
arxiv
Functional Completions of Archimedean Vector Lattices [PDF]
arXiv, 2014 We study completions of Archimedean vector lattices relative to any nonempty set of positively-homogeneous functions on finite-dimensional real vector spaces. Examples of such completions include square mean closed and geometric closed vector lattices, amongst others.
arxiv
The subspace structure of finite dimensional Beidleman near-vector spaces [PDF]
arXiv, 2018 The subspace structure of Beidleman near-vector spaces is investigated. We characterise finite dimensional Beidleman near-vector spaces and we classify the R-subgroups of finite dimensional Beidleman near-vector spaces. We provide an algorithm to compute the smallest R-subgroup containing a given set of vectors.
arxiv
Detection of genuine n-qubit entanglement via the proportionality of two vectors [PDF]
arXiv, 2018 In [Science 340, 1205, 7 June (2013)], via polytopes Michael Walter et al. proposed a sufficient condition detecting the genuinely entangled pure states. In this paper, we indicate that generally, the coefficient vector of a pure product state of $n$ qubits cannot be decomposed into a tensor product of two vectors, and show that a pure state of $n ...
arxiv
Co-occurrence Vectors from Corpora vs. Distance Vectors from Dictionaries [PDF]
COLING94, 304-309., 1995 A comparison was made of vectors derived by using ordinary co-occurrence statistics from large text corpora and of vectors derived by measuring the inter-word distances in dictionary definitions. The precision of word sense disambiguation by using co-occurrence vectors from the 1987 Wall Street Journal (20M total words) was higher than that by using ...
arxiv
Flat Vector Bundles over Parallelizable Manifolds [PDF]
arXiv, 1997 We study flat vector bundles over complex parallelizable manifolds.
arxiv
African Swine Fever Virus Strain Georgia 2007/1 in Ornithodoros erraticus Ticks
Emerging Infectious Diseases, 2012 Adriana V. Diaz +3 more
doaj +1 more source
Can sparse autoencoders be used to decompose and interpret steering vectors? [PDF]
arXivSteering vectors are a promising approach to control the behaviour of large language models. However, their underlying mechanisms remain poorly understood. While sparse autoencoders (SAEs) may offer a potential method to interpret steering vectors, recent findings show that SAE-reconstructed vectors often lack the steering properties of the original ...
arxiv
Existence of periodic orbits for geodesible vector fields on closed 3-manifolds [PDF]
Ergodic Theory Dynam. Systems 30 (2010), no. 6, 1817-1841, 2009 In this paper we deal with the existence of periodic orbits of geodesible vector fields on closed 3-manifolds. A vector field is geodesible if there exists a Riemannian metric on the ambient manifold making its orbits geodesics. In particular, Reeb vector fields and vector fields that admit a global section are geodesible. We will classify the closed 3-
arxiv
Two Novel Mosquitocidal Peptides Isolated from the Venom of the Bahia Scarlet Tarantula (Lasiodora klugi). [PDF]
Toxins (Basel), 2023 Ahmed J +11 more
europepmc +1 more source