We introduce the monic rank of a vector relative to an affine-hyperplane section of an irreducible Zariski-closed affine cone $X$. We show that the monic rank is finite and greater than or equal to the usual $X$-rank. We describe an algorithmic techn...
This code is the implementation of the following paper: M. Jalali, V. Kekatos, N. Gatsis and D. Deka, "Designing Reactive Power Control Rules for Smart Inverters Using Support Vector Machines," in IEEE Transactions on Smart Grid, vol. 11, no. 2, pp. 1759-1770,…
Sent2Vec encoder and training code from the paper "Skip-Thought Vectors" (⭐ 2051)
The optimal beamforming design for multi-user continuous aperture array (CAPA) systems is proposed. In contrast to conventional spatially discrete array (SPDA), the beamformer for CAPA is a continuous function rather than a discrete vector or matrix,...
For a connected graph $G$ with sink vertex $q$, a $G$-parking function is a vector of nonnegative integers whose entries are determined by cut-sets in $G$. Such objects also arise as the superstable configurations in the context of chip-firing. The s...
A Cyber-Physical System (CPS) is defined by its unique characteristics involving both the cyber and physical domains. Their hybrid nature introduces new attack vectors, but also provides an opportunity to design new security defenses. In this paper,...
The fatness of a 4-polytope or 3-sphere is defined as $(f_1+f_2-20)/(f_0+f_3-10)$. We construct arbitrarily fat, strongly regular CW 3-spheres that are both shellable and dual shellable. These spheres have $f$-vectors $(Θ(n),Θ(nα(n)),Θ(nα(n)),Θ...
FutureWave realized the potential for a vector-based web animation tool that might challenge Macromedia Shockwave technology. In 1995, FutureWave modified
Oct 17, 2019 · To give an example, in the derivation of the wave equation from maxwell's equations, the following identity is used: $$ \nabla\times (\nabla\times \mathbf f)=\nabla (\nabla\cdot \mathbf f) …
Look up nabla in Wiktionary, the free dictionary. Nabla may refer to any of the following: the nabla symbol ∇ the vector differential operator, also called
We study the beating effects of solitons in multi-component coupled Bose-Einstein condensate systems. Our analysis indicate that the period of beating behavior is determined by the energy eigenvalue difference in the effective quantum well induced by...
Salas and Garcia introduced the concept of an extended locally convex space in [D. Salas and S. Tapia-Garcia. Extended seminorms and extended topological vector spaces. Topology and its Applications, 2016] which extends the idea of an extended normed...
Biochemical reaction networks are typically modeled by $\dfrac{dx}{dt}=N\cdot K(x)=Y\cdot I_a\cdot K(x)$, with $x$ and $K(x)$ as the concentration and rate vectors, respectively, and $N$, $Y$, and $I_a$ as the stoichiometric, molecularity, and incide...
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum micro-events...
Implied posterior probability of a given model (say, Support Vector Machines (SVM)) at a point $\bf{x}$ is an estimate of the class posterior probability pertaining to the class of functions of the model applied to a given dataset. It can be regarded...
CorelDRAW is a vector graphics editor developed and marketed by Corel Corporation. It is also the name of the Corel graphics suite, which includes the
In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain to the othe...
Motivated by applications to higher-rank Brill-Noether theory and the Bertram-Feinberg-Mukai conjecture, we introduce the concepts of linked alternating and linked symplectic forms on a chain of vector bundles, and show that the linked symplectic Gra...
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time and space...
This paper derives a necessary and sufficient condition for the coincidence of Harmonic residual vectors and the residual vector in GMRES. The properties of the harmonic Ritz values at the stagnation of GMRES were described in the Proposition-4.2 of...