The Relationship Between the Euler Characteristic and the Spectra of Graphs and Networks

2021 ◽  
pp. 487-497
Author(s):  
Michał Ławniczak ◽  
Pavel Kurasov ◽  
Szymon Bauch ◽  
Małgorzata Białous ◽  
Leszek Sirko
Keyword(s):  
Euler Characteristic ◽  
Spectra Of Graphs ◽  
Graphs And Networks ◽  
The Relationship

On the Hamilton Cycle of the Hypercube

2011 ◽  
Vol 480-481 ◽  
pp. 922-927 ◽  
Author(s):  
Yan Zhong Hu ◽  
Hua Dong Wang
Keyword(s):  
Euler Characteristic ◽  
Interconnection Networks ◽  
Cartesian Product ◽  
Hamilton Cycle ◽  
The Other ◽  
Product Graph ◽  
Product Graphs ◽  
Cartesian Product Graphs ◽  
Isomorphic Graphs ◽  
The Relationship

Hypercube is one of the basic types of interconnection networks. In this paper, we use the concept of the Cartesian product graph to define the hypercube Qn, we study the relationship between the isomorphic graphs and the Cartesian product graphs, and we get the result that there exists a Hamilton cycle in the hypercube Qn. Meanwhile, the other properties of the hypercube Qn, such as Euler characteristic and bipartite characteristic are also introduced.

Gaussianization of the spectra of graphs and networks. Theory and applications

2019 ◽  
Vol 470 (2) ◽  
pp. 876-897 ◽  
Author(s):  
Alhanouf Alhomaidhi ◽  
Fawzi Al-Thukair ◽  
Ernesto Estrada
Keyword(s):  
Spectra Of Graphs ◽  
Graphs And Networks

On discrete generalised triangle groups

1995 ◽  
Vol 38 (3) ◽  
pp. 397-412 ◽  
Author(s):  
M. Hagelberg ◽  
C. MacLachlan ◽  
G. Rosenberger
Keyword(s):  
Euler Characteristic ◽  
Discrete Groups ◽  
Triangle Group ◽  
Triangle Groups ◽  
Reduced Word ◽  
Discrete Representations ◽  
Image Position ◽  
The Relationship

A generalised triangle group has a presentation of the formwhere R is a cyclically reduced word involving both x and y. When R = xy, these classical triangle groups have representations as discrete groups of isometrics of S2, R2, H2 depending onIn this paper, for other words R, faithful discrete representations of these groups in Isom +H3 = PSL(2, C) are considered with particular emphasis on the case R = [x, y] and also on the relationship between the Euler characteristic χ and finite covolume representations.

scholarly journals EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY

2012 ◽  
Vol 04 (01) ◽  
pp. 49-70 ◽  
Author(s):  
OMER BOBROWSKI ◽  
MATTHEW STROM BORMAN
Keyword(s):  
Random Field ◽  
Euler Characteristic ◽  
Persistent Homology ◽  
Gaussian Random Field ◽  
Gaussian Random Fields ◽  
Closed Form Expression ◽  
Form Expression ◽  
Kinematic Formula ◽  
Euler Integral ◽  
The Relationship

In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to compute the expected Euler integral of a Gaussian random field using the Gaussian kinematic formula and obtain a simple closed form expression. This results in the first explicitly computable mean of a quantitative descriptor for the persistent homology of a Gaussian random field.

scholarly journals The knot Floer cube of resolutions and the composition product

2020 ◽  
Vol 29 (03) ◽  
pp. 2050006
Author(s):  
Nathan Dowlin
Keyword(s):  
Euler Characteristic ◽  
Floer Homology ◽  
Product Formula ◽  
Knot Floer Homology ◽  
Direct Sum ◽  
Heegaard Diagram ◽  
Composition Product ◽  
The Relationship

We examine the relationship between the oriented cube of resolutions for knot Floer homology and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard diagram for a knot [Formula: see text], we see that the filtered complex decomposes as a direct sum of HOMFLY-PT complexes of various subdiagrams. Applying Jaeger’s composition product formula for knot polynomials, we deduce that the graded Euler characteristic of this direct sum is the HOMFLY-PT polynomial of [Formula: see text].

scholarly journals Euler Characteristic of Graphs and Networks

2021 ◽  
Vol 139 (3) ◽  
pp. 323-327
Author(s):  
M. Lawniczak ◽  
P. Kurasov ◽  
S. Bauch ◽  
M. Białous ◽  
L. Sirko
Keyword(s):  
Euler Characteristic ◽  
Graphs And Networks

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.

Sign in / Sign up

Export Citation Format

Share Document