Topological Measures

2018 ◽  
pp. 631-702
Author(s):  
M. M. Rao
Keyword(s):  
Topological Measures

scholarly journals Topological measures for identifying and predicting the spread of complex contagions

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Douglas Guilbeault ◽  
Damon Centola
Keyword(s):  
Social Networks ◽  
Shortest Path ◽  
Empirical Data ◽  
Path Length ◽  
Centrality Measures ◽  
Social Phenomena ◽  
Node Centrality ◽  
Network Connectedness ◽  
Topological Measures ◽  
Definition Of

AbstractThe standard measure of distance in social networks – average shortest path length – assumes a model of “simple” contagion, in which people only need exposure to influence from one peer to adopt the contagion. However, many social phenomena are “complex” contagions, for which people need exposure to multiple peers before they adopt. Here, we show that the classical measure of path length fails to define network connectedness and node centrality for complex contagions. Centrality measures and seeding strategies based on the classical definition of path length frequently misidentify the network features that are most effective for spreading complex contagions. To address these issues, we derive measures of complex path length and complex centrality, which significantly improve the capacity to identify the network structures and central individuals best suited for spreading complex contagions. We validate our theory using empirical data on the spread of a microfinance program in 43 rural Indian villages.

Topological measures, image transformations and self-similar sets

2005 ◽  
Vol 109 (1-2) ◽  
pp. 65-97 ◽  
Author(s):  
Johan F. Aarnes ◽  
Ørjan Johansen ◽  
Alf B. Rustad
Keyword(s):  
Topological Measures ◽  
Self Similar ◽  
Image Transformations

scholarly journals Topological data analysis and diagnostics of compressible magnetohydrodynamic turbulence

2018 ◽  
Vol 84 (4) ◽  
Author(s):  
I. Makarenko ◽  
P. Bushby ◽  
A. Fletcher ◽  
R. Henderson ◽  
N. Makarenko ◽  
...  
Keyword(s):  
Data Analysis ◽  
Random Fields ◽  
Large Scale ◽  
Betti Numbers ◽  
Mean Field ◽  
Topological Data Analysis ◽  
Topological Measures ◽  
Magnetohydrodynamic Simulations ◽  
Random Flows ◽  
Topological Data

The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical magnetohydrodynamics, it is important to verify that such simulations are in agreement with observations. One of the main challenges in this area is to identify robust quantitative measures to compare structures found in simulations with those inferred from astrophysical observations. A similar challenge is to compare quantitatively results from different simulations. Topological data analysis offers a range of techniques, including the Betti numbers and persistence diagrams, that can be used to facilitate such a comparison. After describing these tools, we first apply them to synthetic random fields and demonstrate that, when the data are standardized in a straightforward manner, some topological measures are insensitive to either large-scale trends or the resolution of the data. Focusing upon one particular astrophysical example, we apply topological data analysis to H iobservations of the turbulent interstellar medium (ISM) in the Milky Way and to recent magnetohydrodynamic simulations of the random, strongly compressible ISM. We stress that these topological techniques are generic and could be applied to any complex, multi-dimensional random field.

Measure in Semigroups

1952 ◽  
Vol 4 ◽  
pp. 396-406 ◽  
Author(s):  
B. R. Gelbaum ◽  
G. K. Kalisch
Keyword(s):  
Topological Group ◽  
Invariant Measure ◽  
Commutative Semigroup ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Counter Example ◽  
Compact Semigroups ◽  
Topological Measures ◽  
Weakened Form ◽  
Locally Compact Semigroups

The major portion of this paper is devoted to an investigation of the conditions which imply that a semigroup (no identity or commutativity assumed) with a bounded invariant measure is a group. We find in §3 that a weakened form of “shearing” is sufficient and a counter-example (§5) shows that “shearing” may not be dispensed with entirely. In §4 we discuss topological measures in locally compact semigroups and find that shearing may be dropped without affecting the results of the earlier sections (Theorem 2). The next two theorems show that under certain circumstances (shearing or commutativity) the topology of the semigroup (already known to be a group by virtue of earlier results) can be weakened so that the structure becomes a separated compact topological group. The last section treats the problem of extending an invariant measure on a commutative semigroup to an invariant measure on its quotient structure.

scholarly journals Topological network measures for drug repositioning

2020 ◽  
Author(s):  
Apurva Badkas ◽  
Sébastien De Landtsheer ◽  
Thomas Sauter
Keyword(s):  
Network Analysis ◽  
Drug Repositioning ◽  
Computational Approaches ◽  
Functional Relationships ◽  
The Past ◽  
Network Measures ◽  
Topological Network ◽  
Topological Measures ◽  
Scope Of Application ◽  
Broad Overview

Abstract Drug repositioning has received increased attention since the past decade as several blockbuster drugs have come out of repositioning. Computational approaches are significantly contributing to these efforts, of which, network-based methods play a key role. Various structural (topological) network measures have thereby contributed to uncovering unintuitive functional relationships and repositioning candidates in drug-disease and other networks. This review gives a broad overview of the topic, and offers perspectives on the application of topological measures for network analysis. It also discusses unexplored measures, and draws attention to a wider scope of application efforts, especially in drug repositioning.

scholarly journals Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake

2016 ◽  
Vol 23 (4) ◽  
pp. 241-256 ◽  
Author(s):  
Eleni Daskalaki ◽  
Konstantinos Spiliotis ◽  
Constantinos Siettos ◽  
Georgios Minadakis ◽  
Gerassimos A. Papadopoulos
Keyword(s):  
Hazard Assessment ◽  
Betweenness Centrality ◽  
Small World ◽  
Clustering Coefficient ◽  
Earthquake Catalog ◽  
Short Term ◽  
2009 L’Aquila Earthquake ◽  
Topological Measures ◽  
Network Properties ◽  
Large Earthquakes

Abstract. The monitoring of statistical network properties could be useful for the short-term hazard assessment of the occurrence of mainshocks in the presence of foreshocks. Using successive connections between events acquired from the earthquake catalog of the Istituto Nazionale di Geofisica e Vulcanologia (INGV) for the case of the L'Aquila (Italy) mainshock (Mw = 6.3) of 6 April 2009, we provide evidence that network measures, both global (average clustering coefficient, small-world index) and local (betweenness centrality) ones, could potentially be exploited for forecasting purposes both in time and space. Our results reveal statistically significant increases in the topological measures and a nucleation of the betweenness centrality around the location of the epicenter about 2 months before the mainshock. The results of the analysis are robust even when considering either large or off-centered the main event space windows.

Geometrical vs topological measures for the evolution of aesthetic maps in a RTS game

2014 ◽  
Vol 5 (4) ◽  
pp. 251-258 ◽  
Author(s):  
R. Lara-Cabrera ◽  
C. Cotta ◽  
A.J. Fernández-Leiva
Keyword(s):  
Topological Measures ◽  
Rts Game
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