Further 2-Dimensional Categorical Structures

2021 ◽  
pp. 513-574
Author(s):  
Niles Johnson ◽  
Donald Yau
Keyword(s):  
Tensor Product ◽  
Double Categories ◽  
Monoidal Bicategories

In this chapter, further 2-dimensional categorical structures are presented and discussed. These include monoidal bicategories, as one-object tricategories, along with braided monoidal bicategories, sylleptic monoidal bicategories, and symmetric monoidal bicategories. The rest of the chapter discusses the Gray tensor product on 2-categories, Gray monoids, double categories, and monoidal double categories.

2-Dimensional Categories

2021 ◽  
Author(s):  
Niles Johnson ◽  
Donald Yau
Keyword(s):  
Tensor Product ◽  
Category Theory ◽  
Basic Category ◽  
Double Categories ◽  
Grothendieck Construction ◽  
Monoidal Bicategories ◽  
Coherence Theorem ◽  
First Time ◽  
Yoneda Lemma

2-Dimensional Categories provides an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a systematic discussion of 2-/bicategories; pasting diagrams; lax functors; 2-/bilimits; the Duskin nerve; the 2-nerve; internal adjunctions; monads in bicategories; 2-monads; biequivalences; the Bicategorical Yoneda Lemma; and the Coherence Theorem for bicategories. Grothendieck fibrations and the Grothendieck construction are discussed next, followed by tricategories, monoidal bicategories, the Gray tensor product, and double categories. Completely detailed proofs of several fundamental but hard-to-find results are presented for the first time. With exercises and plenty of motivation and explanation, this book is useful for both beginners and experts.

Reference Signal Based Tensor Product Expansion for EOG-Related Artifact Separation in EEG

2017 ◽  
Vol E100.A (11) ◽  
pp. 2230-2237
Author(s):  
Akitoshi ITAI ◽  
Arao FUNASE ◽  
Andrzej CICHOCKI ◽  
Hiroshi YASUKAWA
Keyword(s):  
Tensor Product ◽  
Reference Signal

On degeneracy problem of NFSRs via semi-tensor product

2020 ◽  
Author(s):  
Xinyu Zhao ◽  
Biao Wang ◽  
Shuqian Zhu ◽  
Jun-e Feng
Keyword(s):  
Tensor Product ◽  
Degeneracy Problem

On the Buchstaber Subring in MSp∗

1998 ◽  
Vol 5 (5) ◽  
pp. 401-414
Author(s):  
M. Bakuradze
Keyword(s):  
Tensor Product ◽  
Characteristic Classes ◽  
Generalized Quaternion ◽  
Symplectic Cobordisms

Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

scholarly journals Fractal Frames of Functions on the Rectangle

2021 ◽  
Vol 5 (2) ◽  
pp. 42
Author(s):  
María A. Navascués ◽  
Ram Mohapatra ◽  
Md. Nasim Akhtar
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Integrable Function ◽  
Two Dimensional ◽  
Tensor Product Space ◽  
Fractal Functions

In this paper, we define fractal bases and fractal frames of L2(I×J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I×J) with the tensor product space L2(I)⨂L2(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L2(I×J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

Combining improved genetic algorithm and matrix semi-tensor product (STP) in color image encryption

2021 ◽  
Vol 183 ◽  
pp. 108041
Author(s):  
Xiuli Chai ◽  
Xiangcheng Zhi ◽  
Zhihua Gan ◽  
Yushu Zhang ◽  
Yiran Chen ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Tensor Product ◽  
Image Encryption ◽  
Color Image ◽  
Improved Genetic Algorithm ◽  
Color Image Encryption

Nonlinearities in bilingual visual word recognition: An introduction to generalized additive modeling

2021 ◽  
pp. 1-8
Author(s):  
Koji Miwa ◽  
Harald Baayen
Keyword(s):  
Lexical Decision ◽  
Tensor Product ◽  
Nonlinear Interaction ◽  
Mixed Model ◽  
Nonlinear Effects ◽  
Regression Splines ◽  
Generalized Additive Mixed Model ◽  
Generalized Additive Modeling ◽  
Additive Modeling ◽  
Cross Language

Abstract This paper introduces the generalized additive mixed model (GAMM) and the quantile generalized additive mixed model (QGAMM) through reanalyses of bilinguals’ lexical decision data from Dijkstra et al. (2010) and Miwa et al. (2014). We illustrate how regression splines can be used to test for nonlinear effects of cross-language similarity in form as well as for controlling experimental trial effects. We further illustrate the tensor product smooth for a nonlinear interaction between cross-language semantic similarity and word frequency. Finally, we show how the QGAMM helps clarify whether the effect of a particular predictor is constant across distributions of RTs.

scholarly journals A basis for the GLn tensor product algebra

2005 ◽  
Vol 196 (2) ◽  
pp. 531-564 ◽  
Author(s):  
Roger E. Howe ◽  
Eng-Chye Tan ◽  
Jeb F. Willenbring
Keyword(s):  
Tensor Product ◽  
Product Algebra
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