CATEGORIES AS ALGEBRA, II

2003 ◽  
Vol 13 (06) ◽  
pp. 627-703 ◽  
Author(s):  
BENJAMIN STEINBERG ◽  
BRET TILSON
Keyword(s):  
Semidirect Product ◽  
Derived Category ◽  
Algebra Ii ◽  
Decomposition Formula ◽  
Traditional Setting ◽  
The Relationship ◽  
Relational Morphism ◽  
Straightforward Proof

A theory of the semidirect product of categories and the derived category of a category morphism is presented. In order to include division (≺) in this theory, the traditional setting of these constructions is expanded to include relational arrows. In this expanded setting, a relational morphism φ : M → N of categories determines an optimal decomposition [Formula: see text] where [Formula: see text] denotes semidirect product and D(φ) is the derived category of φ.The theory of the semidirect product of varieties of categories, V * W, is developed. Associated with each variety V of categories is the collection [Formula: see text] of relational morphisms whose derived category belongs to V. The semidirect product of varieties and the composition of classes of the form [Formula: see text] are shown to stand in the relationship [Formula: see text] The associativity of the semidirect product of varieties follows from this result.Finally, it is demonstrated that all the results in the article concerning varieties of categories have pseudovariety and monoidal versions. This allows us to furnish a straightforward proof that [Formula: see text] for both varieties and pseudovarieties of monoids.

ON THE AUTOMORPHISM GROUPS OF A FAMILY OF BINARY QUANTUM ERROR-CORRECTING CODES

2006 ◽  
Vol 04 (06) ◽  
pp. 1013-1022
Author(s):  
TAILIN LIU ◽  
FENGTONG WEN ◽  
QIAOYAN WEN
Keyword(s):  
Semidirect Product ◽  
Automorphism Groups ◽  
Error Correcting Code ◽  
Error Correcting Codes ◽  
Index Formula ◽  
Product Group ◽  
Simplex Code ◽  
Quantum Error ◽  
The Relationship ◽  
Free Element

Based on the classical binary simplex code [Formula: see text] and any fixed-point-free element f of [Formula: see text], Calderbank et al. constructed a binary quantum error-correcting code [Formula: see text]. They proved that [Formula: see text] has a normal subgroup H, which is a semidirect product group of the centralizer Z(f) of f in GLm(2) with [Formula: see text], and the index [Formula: see text] is the number of elements of Ff = {f, 1 - f, 1/f, 1 - 1/f, 1/(1 - f), f/(1 - f)} that are conjugate to f. In this paper, a theorem to describe the relationship between the quotient group [Formula: see text] and the set Ff is presented, and a way to find the elements of Ff that are conjugate to f is proposed. Then we prove that [Formula: see text] is isomorphic to S3 and H is a semidirect product group of [Formula: see text] with [Formula: see text] in the linear case. Finally, we generalize a result due to Calderbank et al.

scholarly journals Videos in Online Courses

2022 ◽  
Vol 4 (3) ◽  
pp. 94-110
Author(s):  
Eric Litton
Keyword(s):  
Quantitative Analysis ◽  
Student Engagement ◽  
Student Performance ◽  
Online Courses ◽  
Course Content ◽  
Analysis Techniques ◽  
Video Viewing ◽  
Online Videos ◽  
Traditional Setting ◽  
The Relationship

Many instructors use videos to support their teaching in online courses to convey course content that would normally be taught in a traditional setting. Prior studies have shown some connection between utilizing online videos and student performance but do not always support their finding statistically or consider the nuance of the online videos, such as if the videos are required and how long the videos are. This article uses various quantitative analysis techniques to investigate the relationship between video length, student video viewing patterns, and grades. The findings indicate that videos should stay within a certain length to encourage student engagement with the videos and course assignments. Also, watching online videos is only positively related to grades when students are not required to watch, a result that is consistent across course-level and student-level models. Student viewing patterns also differ for courses that require watching videos versus those that do not. The article concludes by discussing the relevance of these results and how instructors can best utilize online videos in their courses.

Regulating worker-customer relations to improve workers’ wellbeing

2019 ◽  
Vol 10 (2) ◽  
pp. 154-162
Author(s):  
Chris Wuytens ◽  
Sarah De Groof
Keyword(s):  
Customer Relations ◽  
Need Satisfaction ◽  
Continuous Measure ◽  
Labour Law ◽  
Gig Economy ◽  
Recent Developments ◽  
Labour Legislation ◽  
Traditional Setting ◽  
The Impact ◽  
The Relationship

Recent developments in the gig economy triggered labour law. Platforms change the relationship between customers and workers causing over-subordination of workers. The over-subordination is caused by customers and the surveys they complete to evaluate the worker. The influence of customers over workers can also be seen in a more traditional setting. However, customers are not always king. It is suggested in this article that surveys can be used as an instrument to build decent labour relationships. Installing the measurement of needs measures the impact of customers on workers. By installing a continuous measure of the needs, we have at our disposal an instrument to fulfil labour law’s wellbeing function. Labour legislation could oblige employers to integrate need satisfaction into their customer surveys and their workers surveys. By doing so, technology allows us to make sure that platform work or any kind of work where workers meet high customer demands, become ‘Innovative forms of work that ensure quality working conditions’, as requested by the European Social Pillar.

Expansions of completely simple semigroups

2004 ◽  
Vol 41 (1) ◽  
pp. 39-58
Author(s):  
B. Billhardt
Keyword(s):  
Semidirect Product ◽  
Simple Semigroup ◽  
Completely Simple Semigroup ◽  
Completely Simple Semigroups ◽  
Group 6 ◽  
The Relationship ◽  
Completely Simple

For any completely simple semigroup C a regular expansion S(C) is constructed which is the Birget-Rhodes prefix expansion CPr if C is a group [6]. We show that our construction generalizes two important features of CPr. Moreover we embed S (C) into a restricted semidirect product of a semilattice by C and investigate the relationship to the expansion P(C), introduced by Meakin [14].

m-Noncrossing trees

2018 ◽  
Vol 17 (10) ◽  
pp. 1850187 ◽  
Author(s):  
Kiyoshi Igusa
Keyword(s):  
Representation Theory ◽  
Derived Category ◽  
Point Of View ◽  
Module Category ◽  
Cluster Category ◽  
Cluster Theory ◽  
Type Formula ◽  
Exceptional Sequences ◽  
The Relationship

We examine [Formula: see text]-cluster theory from an elementary point of view using a generalization of [Formula: see text]-ary trees which we call [Formula: see text]-noncrossing trees. We show that these trees are in bijection with [Formula: see text]-clusters in the [Formula: see text]-cluster category of a quiver of type [Formula: see text]. Similar trees are in bijection with complete exceptional sequences. Most of this paper is expository, explaining definitions and known results about these topics in representation theory. One application of these trees is that the mutation formula for [Formula: see text]-clusters is derived from the more elementary mutation of trees. The main new result is that the natural map of an [Formula: see text]-noncrossing tree into the plane is an embedding. We also explain the relationship between [Formula: see text]-noncrossing trees and finite Harder–Narasimhan systems in the derived category of the module category of type [Formula: see text].

Interstellar gas in the central region of the Galaxy

1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr
Keyword(s):  
Central Region ◽  
Galactic Plane ◽  
Neutral Hydrogen ◽  
Continuum Emission ◽  
Galactic Centre ◽  
Interstellar Gas ◽  
Hydrogen Recombination ◽  
The Galaxy ◽  
Centre Region ◽  
The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

Choosing a Markov blanket

2020 ◽  
Vol 43 ◽  
Author(s):  
Thomas Parr
Keyword(s):  
Markov Blanket ◽  
Target Article ◽  
The Relationship

Abstract This commentary focuses upon the relationship between two themes in the target article: the ways in which a Markov blanket may be defined and the role of precision and salience in mediating the interactions between what is internal and external to a system. These each rest upon the different perspectives we might take while “choosing” a Markov blanket.

Tinkering with cognitive gadgets: Cultural evolutionary psychology meets active inference

2019 ◽  
Vol 42 ◽  
Author(s):  
Paul Benjamin Badcock ◽  
Axel Constant ◽  
Maxwell James Désormeau Ramstead
Keyword(s):  
Evolutionary Psychology ◽  
Research Program ◽  
Active Inference ◽  
Innovative Research ◽  
Cognitive Faculties ◽  
Cultural Evolutionary ◽  
The Relationship

Abstract Cognitive Gadgets offers a new, convincing perspective on the origins of our distinctive cognitive faculties, coupled with a clear, innovative research program. Although we broadly endorse Heyes’ ideas, we raise some concerns about her characterisation of evolutionary psychology and the relationship between biology and culture, before discussing the potential fruits of examining cognitive gadgets through the lens of active inference.

Radiation Damage, Contrast and Statistics in High Resolution Biological Electron Microscopy

1970 ◽  
Vol 28 ◽  
pp. 260-261
Author(s):  
Robert M. Glaeser
Keyword(s):  
High Resolution ◽  
Particle Flux ◽  
Unit Area ◽  
Signal To Noise ◽  
Resolution Image ◽  
High Resolution Image ◽  
Pass Through ◽  
Counting Statistics ◽  
The Relationship ◽  
Picture Element

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.

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