How directed is a directed network?

The trophic levels of nodes in directed networks can reveal their functional properties. Moreover, the trophic coherence of a network, defined in terms of trophic levels, is related to properties such as cycle structure, stability and percolation. The standard definition of trophic levels, however, borrowed from ecology, suffers from drawbacks such as requiring basal nodes, which limit its applicability. Here we propose simple improved definitions of trophic levels and coherence that can be computed on any directed network. We demonstrate how the method can identify node function in examples including ecosystems, supply chain networks, gene expression and global language networks. We also explore how trophic levels and coherence relate to other topological properties, such as non-normality and cycle structure, and show that our method reveals the extent to which the edges in a directed network are aligned in a global direction.

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A Note on Topological Properties of Non-Hausdorff Manifolds

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2009/891785 ◽

2009 ◽

Vol 2009 ◽

pp. 1-4

Author(s):

Steven L. Kent ◽

Roy A. Mimna ◽

Jamal K. Tartir

Keyword(s):

Topological Space ◽

The Other ◽

Topological Manifold ◽

Topological Properties ◽

Countable Base ◽

Standard Definition ◽

Hausdorff Topological Space ◽

Definition Of

The notion of compatible apparition points is introduced for non-Hausdorff manifolds, and properties of these points are studied. It is well known that the Hausdorff property is independent of the other conditions given in the standard definition of a topological manifold. In much of literature, a topological manifold of dimension is a Hausdorff topological space which has a countable base of open sets and is locally Euclidean of dimension . We begin with the definition of a non-Hausdorff topological manifold.

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A practical metric for melanopic metrology

Lighting Research and Technology ◽

10.1177/1477153518824147 ◽

2019 ◽

Vol 51 (8) ◽

pp. 1178-1191 ◽

Cited By ~ 4

Author(s):

SM Berman ◽

RD Clear

Keyword(s):

Ganglion Cell ◽

Retinal Ganglion Cell ◽

Vision Research ◽

Spectral Response ◽

Retinal Ganglion ◽

Standard Definition ◽

Standard Unit ◽

Vision Science ◽

The Past ◽

Definition Of

Over the past decade, there has been a growing interest in lighting research on the effects of the recently discovered melanopsin receptor (also referred to as the intrinsically photosensitive retinal ganglion cell) and its impacts on health and vision. Presently, there is not a generally accepted metrology for dealing with the spectral response of the melanopsin receptor as applied to both lighting and vision research. A proposition to handle this issue from a vision science perspective has been presented in 2014 in the journal Trends in Neurosciences and from a more lighting perspective in 2017 in Lighting Research and Technology. These propositions are complex, and do not retain the CIE standard definition of a lumen. In this paper, we propose an approach based on effective watts and melanopic/photopic ratios that is both simpler and more closely aligned with CIE standard unit definitions. In addition, we include some practical examples of how such ratios are accessible now, and can be used for both lighting and vision research as well as applications.

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Feynman diagrams and rooted maps

Open Physics ◽

10.1515/phys-2018-0023 ◽

2018 ◽

Vol 16 (1) ◽

pp. 149-167 ◽

Cited By ~ 6

Author(s):

Andrea Prunotto ◽

Wanda Maria Alberico ◽

Piotr Czerski

Keyword(s):

Single Particle ◽

Feynman Diagram ◽

Feynman Diagrams ◽

Topological Properties ◽

Many Body ◽

Perturbative Order ◽

Original Definition ◽

Many Body Systems ◽

Definition Of ◽

Particle Propagator

Abstract The rooted maps theory, a branch of the theory of homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.

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Gene insulation. Part II: natural strategies in vertebrates

Biochemistry and Cell Biology ◽

10.1139/o10-111 ◽

2010 ◽

Vol 88 (6) ◽

pp. 885-898 ◽

Cited By ~ 8

Author(s):

Michèle Amouyal

Keyword(s):

Gene Expression ◽

Dna Methylation ◽

Protein Interactions ◽

Dna Looping ◽

Chromatin Domain ◽

Trna Genes ◽

Binding Factor ◽

Genomic Environment ◽

Nuclear Structures ◽

Definition Of

The way a gene is insulated from its genomic environment in vertebrates is not basically different from what is observed in yeast and Drosophila (preceding article in this issue). If the formation of a looped chromatin domain, whether generated by attachment to the nuclear matrix or not, has become a classic way to confine an enhancer to a specific genomic domain and to coordinate, sequentially or simultaneously, gene expression in a given program, its role has been extended to new networks of genes or regulators within the same gene. A wider definition of the bases of the chromatin loops (nonchromosomal nuclear structures or genomic interacting elements) is also available. However, whereas insulation in Drosophila is due to a variety of proteins, in vertebrates insulators are still practically limited to CTCF (the CCCTC-binding factor), which appears in all cases to be the linchpin of an architecture that structures the assembly of DNA–protein interactions for gene regulation. As in yeast and Drosophila, the economy of means is the rule and the same unexpected diversion of known transcription elements (active or poised RNA polymerases, TFIIIC elements out of tRNA genes, permanent histone replacement) is observed, with variants peculiar to CTCF. Thus, besides structuring DNA looping, CTCF is a barrier to DNA methylation or interferes with all sorts of transcription processes, such as that generating heterochromatin.

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Cycle and flow trusses in directed networks

Royal Society Open Science ◽

10.1098/rsos.160270 ◽

2016 ◽

Vol 3 (11) ◽

pp. 160270 ◽

Cited By ~ 5

Author(s):

Taro Takaguchi ◽

Yuichi Yoshida

Keyword(s):

Truss Structures ◽

Directed Network ◽

Unified Framework ◽

Directed Networks ◽

Research Fields ◽

Wide Range ◽

Definition Of ◽

Information Finding ◽

Empirical Networks ◽

Module Structures

When we represent real-world systems as networks, the directions of links often convey valuable information. Finding module structures that respect link directions is one of the most important tasks for analysing directed networks. Although many notions of a directed module have been proposed, no consensus has been reached. This lack of consensus results partly because there might exist distinct types of modules in a single directed network, whereas most previous studies focused on an independent criterion for modules. To address this issue, we propose a generic notion of the so-called truss structures in directed networks. Our definition of truss is able to extract two distinct types of trusses, named the cycle truss and the flow truss, from a unified framework. By applying the method for finding trusses to empirical networks obtained from a wide range of research fields, we find that most real networks contain both cycle and flow trusses. In addition, the abundance of (and the overlap between) the two types of trusses may be useful to characterize module structures in a wide variety of empirical networks. Our findings shed light on the importance of simultaneously considering different types of modules in directed networks.

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The Humdrum Use of Ultimate Authority: Defining and Analysing Chapter VII Resolutions

Nordic Journal of International Law ◽

10.1163/090273509x12448190941129 ◽

2009 ◽

Vol 78 (3) ◽

pp. 309-342 ◽

Cited By ~ 6

Author(s):

Patrik Johansson

Keyword(s):

Cold War ◽

United Nations ◽

Security Council ◽

Security Council Resolution ◽

Post Cold War ◽

Standard Definition ◽

The Status ◽

Definition Of ◽

The Cold War ◽

Business As Usual

AbstractUnder Chapter VII of the Charter of the United Nations, the Security Council has the unique authority to make decisions that are binding on member states. However, the lack of a standard definition of what makes a Security Council resolution "a Chapter VII resolution" has caused disagreement regarding the status of several resolutions. This is unfortunate as the international community should never have to doubt whether a Security Council resolution is in fact adopted under Chapter VII or not. It is also unnecessary. This article addresses this problem by proposing a definition of Chapter VII resolutions, based on two criteria referred to as "Article 39 determinations" and "Chapter VII decisions". On the basis of the proposed definition, the article describes and analyses a dramatic increase in the use of Chapter VII during the post-Cold War era. It concludes that as Chapter VII has come to constitute the majority of Security Council resolutions in recent years, the resort to Chapter VII no longer signifies exceptional determination and resolve, which it did during the Cold War; instead Chapter VII today implies business as usual. An appendix lists all Chapter VII resolutions from 1946–2008.

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The Standard Definition of Magic Matrix

Advances in Applied Mathematics ◽

10.12677/aam.2021.108282 ◽

2021 ◽

Vol 10 (08) ◽

pp. 2714-2724

Author(s):

兴祥刘

Keyword(s):

Standard Definition ◽

Definition Of

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Comment on a Standard Definition of Response Rates

Journal of Marketing Research ◽

10.2307/3151610 ◽

1984 ◽

Vol 21 (3) ◽

pp. 336 ◽

Cited By ~ 54

Author(s):

Frederick Wiseman ◽

Maryann Billington

Keyword(s):

Response Rates ◽

Standard Definition ◽

Definition Of

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Tongue Thrust: A Point of View

Journal of Speech and Hearing Disorders ◽

10.1044/jshd.4102.172 ◽

1976 ◽

Vol 41 (2) ◽

pp. 172-184 ◽

Cited By ~ 2

Author(s):

Marvin L. Hanson

Keyword(s):

Orthodontic Treatment ◽

Point Of View ◽

Patient Age ◽

Present Evidence ◽

Standard Definition ◽

Myofunctional Therapy ◽

Developmental Factors ◽

Patient Âgé ◽

Definition Of ◽

Tongue Thrust

The purpose of the present paper is to present evidence to support the following hypotheses: (1) there is a relationship between tongue thrust and malocclusion, and it is probably a reciprocal one; (2) tongue thrust may yield spontaneously to nonthrusting patterns; (3) if tongue thrust does not yield spontaneously to nonthrusting patterns, some form of treatment should be considered; (4) if myofunctional therapy is the treatment of choice, its timing with respect to patient age, developmental factors, and orthodontic treatment should be an individual matter. The need for more definitive research is described. In order for such research to be meaningful, a standard definition of tongue thrust is required. Such a definition is proposed.

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