In mathematics, for positive integers k and s, a vectorial addition chain is a sequence V of k-dimensional vectors vi of nonnegative integers for −k +
We initiate the study of multi-attribute group fairness in $k$-nearest neighbor ($k$-NN) search over vector databases. Unlike prior work that optimizes efficiency or query filtering, fairness imposes count constraints to ensure proportional represent...
This paper presents the implementation of polynomial vector back propagation algorithm (PVBPA) for estimating the power, torque, specific fuel consumption and presence of carbon monoxide, hydrocarbons in the emission of a direct injection diesel engi...
A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hype...
A method based on one class support vector machine (OCSVM) is proposed for class incremental learning. Several OCSVM models divide the input space into several parts. Then, the 1VS1 classifiers are constructed for the confuse part by using the suppor...
The Relevance Vector Machine (RVM) is a recently developed machine learning framework capable of building simple models from large sets of candidate features. Here, we describe a protocol for using the RVM to explore very large numbers of candidate...
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We introduce the concept of "Legal Zero-Days" as a novel risk vector for advanced AI systems. Legal Zero-Days are previously undiscovered vulnerabilities in legal frameworks that, when exploited, can cause immediate and significant societal disruptio...
Scalable Vector Graphics (SVG) is an XML-based vector graphics format for defining two-dimensional graphics, having support for interactivity and animation
Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as
Integration of scalar and vector visualization has been an interesting topic. This paper presents a technique to appropriately select and display multiple streamlines while overlaying with isosurfaces, aiming an integrated scalar and vector field vis...
Torque vectoring is a technology employed in automobile differentials that has the ability to vary the torque to each half-shaft with an electronic system;
or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by ∇ (the nabla symbol)
In this paper, we prove that the world of near-vector spaces allows us to work with non-linear problems and yet, gives access to most of the tools linear algebra has to offer. We establish some fundamental results for near-vector spaces toward extend...
May 10, 2007 · A rank 3 tensor inputs three generalized vectors (i.e. either a vector or their dual vector), and spits out a scalar. One can also think of it as inputting 2 generalized vectors (or a rank 2 tensor), …
Every tensor is associated with a linear map that produces a scalar. For instance, a vector can be identified with a map that takes in another vector (in the presence of an inner product) and produces …
Feb 11, 2024 · A tensor extends the notion of a matrix analogous to how a vector extends the notion of a scalar and a matrix extends the notion of a vector. A tensor can have any number of dimensions, …
Jun 18, 2017 · Tensor Product Properties Definition: A tensor product of vector spaces is a vector space structure on the Cartesian product that satisfies This means a tensor product is a freely generated …
This work describes the R package GET that implements global envelopes for a general set of $d$-dimensional vectors $T$ in various applications. A $100(1-α)$% global envelope is a band bounded by two vectors such that the probability that $T$ falls...
We prove new non-existence results for vectorial monomial Dillon type bent functions mapping the field of order $2^{2m}$ to the field of order $2^{m/3}$. When $m$ is odd and $m>3$ we show that there are no such functions. When $m$ is even we derive a...