scholarly journals Five-dimensional vector multiplets in arbitrary signature

2018 ◽  
Vol 2018 (9) ◽  
Author(s):  
L. Gall ◽  
T. Mohaupt
Keyword(s):  
Dimensional Vector ◽  
Arbitrary Signature

scholarly journals Four-dimensional vector multiplets in arbitrary signature (I)

2020 ◽  
Vol 17 (10) ◽  
pp. 2050150 ◽  
Author(s):  
V. Cortés ◽  
L. Gall ◽  
T. Mohaupt
Keyword(s):  
Vector Space ◽  
Classification Problem ◽  
Lie Superalgebras ◽  
Symmetry Groups ◽  
Sufficient Condition ◽  
Dimensional Vector ◽  
Necessary And Sufficient Condition ◽  
Arbitrary Signature ◽  
Necessary And Sufficient ◽  
R Symmetry

We derive a necessary and sufficient condition for Poincaré Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the Schur group on the vector space of superbrackets. We then classify four-dimensional [Formula: see text] supersymmetry algebras, which are found to be unique in Euclidean and in neutral signature, while in Lorentz signature there exist two algebras with R-symmetry groups [Formula: see text] and [Formula: see text], respectively.

Four-dimensional vector multiplets in arbitrary signature (II)

2020 ◽  
Vol 17 (10) ◽  
pp. 2050151 ◽  
Author(s):  
V. Cortés ◽  
L. Gall ◽  
T. Mohaupt
Keyword(s):  
Dimensional Reduction ◽  
Companion Paper ◽  
Lie Superalgebras ◽  
Dimensional Vector ◽  
Vector Multiplet ◽  
Four Dimensions ◽  
Underlying Space ◽  
Arbitrary Signature ◽  
Minkowski Signature ◽  
Field Redefinition

Following the classification up to isomorphism of [Formula: see text] Poincaré Lie superalgebras in four dimensions with arbitrary signature obtained in a companion paper, we present off-shell vector multiplet representations and invariant Lagrangians realizing these algebras. By dimensional reduction of five-dimensional off-shell vector multiplets, we obtain two representations in each four-dimensional signature. In Euclidean and neutral signature, these representations can be mapped to each other by a field redefinition induced by the action of the Schur group on the space of superbrackets. In Minkowski signature, we show that the superbrackets underlying the two vector multiplet representations belong to distinct open orbits of the Schur group and are therefore inequivalent. Our formalism allows to answer questions about the possible relative signs between terms in the Lagrangian systematically by relating them to the underlying space of superbrackets.

Model Based Defect Detection in Multi-Dimensional Vector Spaces

2011 ◽  
Vol 131 (9) ◽  
pp. 1633-1641
Author(s):  
Toshifumi Honda ◽  
Kenji Obara ◽  
Minoru Harada ◽  
Hajime Igarashi
Keyword(s):  
Defect Detection ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Model Based

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

scholarly journals Tropical Balls and Its Applications to K Nearest Neighbor over the Space of Phylogenetic Trees

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 779
Author(s):  
Ruriko Yoshida
Keyword(s):  
Supervised Learning ◽  
Phylogenetic Trees ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
High Dimensional ◽  
Learning Method ◽  
Dimensional Vector ◽  
K Nearest Neighbor ◽  
K Nearest Neighbors

A tropical ball is a ball defined by the tropical metric over the tropical projective torus. In this paper we show several properties of tropical balls over the tropical projective torus and also over the space of phylogenetic trees with a given set of leaf labels. Then we discuss its application to the K nearest neighbors (KNN) algorithm, a supervised learning method used to classify a high-dimensional vector into given categories by looking at a ball centered at the vector, which contains K vectors in the space.

scholarly journals A divide-and-conquer algorithm for quantum state preparation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Israel F. Araujo ◽  
Daniel K. Park ◽  
Francesco Petruccione ◽  
Adenilton J. da Silva
Keyword(s):  
Computational Cost ◽  
Quantum Circuit ◽  
Divide And Conquer ◽  
Computational Time ◽  
Quantum Computers ◽  
Dimensional Vector ◽  
Quantum Devices ◽  
Divide And Conquer Algorithm ◽  
Quantum State Preparation ◽  
Quantum Device

AbstractAdvantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

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