Large-Batch and Multi-Structure Group Targets Tracking Based on Serial GLMB

2021 ◽  
Author(s):  
Zhi Zhao ◽  
Weifeng Liu ◽  
Sen Wang ◽  
Shibo Gao
Keyword(s):  
Structure Group ◽  
Large Batch

scholarly journals Yang–Mills connections on compact complex tori

2015 ◽  
Vol 07 (02) ◽  
pp. 293-307
Author(s):  
Indranil Biswas
Keyword(s):  
Algebraic Group ◽  
Maximal Compact Subgroup ◽  
Compact Subgroup ◽  
Structure Group ◽  
Kähler Structure ◽  
Yang Mills ◽  
Complex Torus ◽  
Complex Tori

Let G be a connected reductive complex affine algebraic group and K ⊂ G a maximal compact subgroup. Let M be a compact complex torus equipped with a flat Kähler structure and (EG, θ) a polystable Higgs G-bundle on M. Take any C∞ reduction of structure group EK ⊂ EG to the subgroup K that solves the Yang–Mills equation for (EG, θ). We prove that the principal G-bundle EG is polystable and the above reduction EK solves the Einstein–Hermitian equation for EG. We also prove that for a semistable (respectively, polystable) Higgs G-bundle (EG, θ) on a compact connected Calabi–Yau manifold, the underlying principal G-bundle EG is semistable (respectively, polystable).

SYMMETRIES OF CERTAIN PHYSICAL THEORIES AND THE JORDAN ALGEBRAS

1992 ◽  
Vol 07 (15) ◽  
pp. 3623-3637 ◽  
Author(s):  
R. FOOT ◽  
G. C. JOSHI
Keyword(s):  
Jordan Algebra ◽  
Space Time ◽  
Jordan Algebras ◽  
Bosonic String ◽  
The Other ◽  
Structure Group ◽  
Division Algebras ◽  
Hermitian Matrices ◽  
Higher Dimensional ◽  
Algebraic Framework

It is shown that the sequence of Jordan algebras [Formula: see text], whose elements are the 3 × 3 Hermitian matrices over the division algebras ℝ, [Formula: see text], ℚ and [Formula: see text], can be associated with the bosonic string as well as the superstring. The construction reveals that the space–time symmetries of the first-quantized bosonic string and superstring actions can be related. The bosonic string and the superstring are associated with the exceptional Jordan algebra while the other Jordan algebras in the [Formula: see text] sequence can be related to parastring theories. We then proceed to further investigate a connection between the symmetries of supersymmetric Lagrangians and the transformations associated with the structure group of [Formula: see text]. The N = 1 on-shell supersymmetric Lagrangians in 3, 4 and 6-dimensions with a spin 0 field and a spin 1/2 field are incorporated within the Jordan-algebraic framework. We also make some remarks concerning a possible role for the division algebras in the construction of higher-dimensional extended objects.

scholarly journals Why Does Large Batch Training Result in Poor Generalization? A Comprehensive Explanation and a Better Strategy from the Viewpoint of Stochastic Optimization

2018 ◽  
Vol 30 (7) ◽  
pp. 2005-2023 ◽  
Author(s):  
Tomoumi Takase ◽  
Satoshi Oyama ◽  
Masahito Kurihara
Keyword(s):  
Gradient Descent ◽  
Optimization Problems ◽  
Descent Method ◽  
Batch Size ◽  
Gradient Descent Method ◽  
Neural Network Training ◽  
Nonconvex Optimization Problems ◽  
Large Batch ◽  
Network Training ◽  
Comprehensive Framework

We present a comprehensive framework of search methods, such as simulated annealing and batch training, for solving nonconvex optimization problems. These methods search a wider range by gradually decreasing the randomness added to the standard gradient descent method. The formulation that we define on the basis of this framework can be directly applied to neural network training. This produces an effective approach that gradually increases batch size during training. We also explain why large batch training degrades generalization performance, which previous studies have not clarified.

scholarly journals Deformation quantization of principal bundles

2016 ◽  
Vol 13 (08) ◽  
pp. 1630010
Author(s):  
Paolo Aschieri
Keyword(s):  
Quantum Group ◽  
Deformation Quantization ◽  
Principal Bundle ◽  
Base Space ◽  
Structure Group ◽  
Galois Extensions ◽  
Principal Bundles ◽  
Group Of Automorphisms ◽  
Drinfeld Twist

We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles and, more in general, to the deformation of Hopf–Galois extensions. First, we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next, we twist deform a subgroup of the group of automorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations, we obtain noncommutative principal bundles with noncommutative fiber and base space as well.

scholarly journals The measure-theoretic structure group is not invariant

1977 ◽  
Vol 21 (1) ◽  
pp. 178-184 ◽  
Author(s):  
Russell A. Johnson
Keyword(s):  
Structure Group
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