scholarly journals Classification of book representations of K6

2017 ◽  
Vol 26 (12) ◽  
pp. 1750075
Author(s):  
Dana Rowland
Keyword(s):  
Complete Graph ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Crossing Number ◽  
Ambient Isotopy ◽  
Three Dimensional Space

A book representation of a graph is a particular way of embedding a graph in three-dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to [Formula: see text], the complete graph with six vertices. We prove there are exactly 59 distinct book representations for [Formula: see text], and we identify the number and type of knotted and linked cycles in each representation. We show that book representations of [Formula: see text] contain between one and seven links, and up to nine knotted cycles. Furthermore, all links and cycles in a book representation of [Formula: see text] have crossing number at most four.

scholarly journals How Can I Grab That?

i-com ◽  
2020 ◽  
Vol 19 (2) ◽  
pp. 67-85
Author(s):  
Matthias Weise ◽  
Raphael Zender ◽  
Ulrike Lucke
Keyword(s):  
Virtual Reality ◽  
User Experience ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Advantages And Disadvantages ◽  
Multiple Dimensions ◽  
Application Developers ◽  
Three Dimensional Space

AbstractThe selection and manipulation of objects in Virtual Reality face application developers with a substantial challenge as they need to ensure a seamless interaction in three-dimensional space. Assessing the advantages and disadvantages of selection and manipulation techniques in specific scenarios and regarding usability and user experience is a mandatory task to find suitable forms of interaction. In this article, we take a look at the most common issues arising in the interaction with objects in VR. We present a taxonomy allowing the classification of techniques regarding multiple dimensions. The issues are then associated with these dimensions. Furthermore, we analyze the results of a study comparing multiple selection techniques and present a tool allowing developers of VR applications to search for appropriate selection and manipulation techniques and to get scenario dependent suggestions based on the data of the executed study.

GRAPH INVARIANTS AND THE TOPOLOGY OF RNA FOLDING

1994 ◽  
Vol 03 (03) ◽  
pp. 233-245 ◽  
Author(s):  
LOUIS H. KAUFFMAN ◽  
YURI MAGARSHAK
Keyword(s):  
Rna Folding ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Graph Embeddings ◽  
Graph Invariants ◽  
Vassiliev Invariants ◽  
Ambient Isotopy ◽  
Molecular Folding ◽  
General Method ◽  
Three Dimensional Space

A new general method is described for obtaining ambient isotopy or regular isotopy invariants of even valence rigid vertex graphs embedded in three-dimensional space. The paper concentrates on the case of 4-valent vertices and defines an RNA vertex in analogy to the structure of a folded molecule. Examples are given to show how these methods can discriminate graph embeddings that are indistinguishable via Vassiliev invariants. Applications to molecular folding are discussed.

scholarly journals A Clustering Method Applied to the Analysis of Planetary Nebulae

1993 ◽  
Vol 155 ◽  
pp. 44-44
Author(s):  
O.S. Yatsyk
Keyword(s):  
Planetary Nebula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Planetary Nebulae ◽  
Spectral Lines ◽  
Radio Flux ◽  
Clustering Method ◽  
Centroid Method ◽  
Three Dimensional Space

Intensities of the observed spectral lines, radio fluxes and Hβ fluxes are used for the classification of planetary nebulae by centroid method of taxonomical analysis. Two variants of classification are proposed. The first one– in the three–dimensional space of relation of intensity of spectral lines He II λ 4686/HeI λ 4471, [OIII] λ 4959+5007/[OII] λ 3726+29, [OIII] λ 4959+5007/[OIII] 4363. The second variants is the classification in the three-dimensional space with cooordinates being radio flux, Hβ flux and [OIII] λ 4959+5007 intensity. The membership of classes (taxons) are presented. In the diagram joining the planetary nebula descriptors pairwise there are regions of complete (or predominant) of nebulae belonging to the same taxon, but there are also some regions of overlap. The corresponding taxons are not isolated but merge continuously into one another.

scholarly journals Application of methods of multidimensional statistical analysis for the classification of signal fragments during cutting processing

2021 ◽  
Vol 2091 (1) ◽  
pp. 012073
Author(s):  
A V Belov ◽  
N N Trufanov ◽  
D V Churikov ◽  
O V Kravchenko
Keyword(s):  
Spectral Analysis ◽  
Statistical Analysis ◽  
Vector Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Vibration Sensor ◽  
Average Amplitude ◽  
Average Value ◽  
Three Dimensional Space

Abstract The preliminary processing of the signal coming from the vibration sensor is performed. Spectral analysis methods allow identifying the distinctive zones corresponding to three parameters: the average amplitude of vibrations, the average value of the spectrum, and the complex parameter of the vibration density obtained using interpolation methods. Hence, the vector contains the listed parameters as components produce a vector space, and the equations of separating surfaces in three-dimensional space and classification errors are calculated.

scholarly journals Emotion Recognition: An Evaluation of ERP Features Acquired from Frontal EEG Electrodes

2021 ◽  
Vol 11 (9) ◽  
pp. 4131
Author(s):  
Moon Inder Singh ◽  
Mandeep Singh
Keyword(s):  
Dimensional Space ◽  
Brain Computer Interface ◽  
Three Dimensional ◽  
Event Related Potential ◽  
Computer Interface ◽  
Two Dimensional ◽  
Emotion Classification ◽  
Better Than ◽  
Three Dimensional Space

The challenge to develop an affective Brain Computer Interface requires the understanding of emotions psychologically, physiologically as well as analytically. To make the analysis and classification of emotions possible, emotions have been represented in a two-dimensional or three-dimensional space represented by arousal and valence domains or arousal, valence and dominance domains, respectively. This paper presents the classification of emotions into four classes in an arousal–valence plane using the orthogonal nature of emotions. The average Event Related Potential (ERP) attributes and differential of average ERPs acquired from the frontal region of 24 subjects have been used to classify emotions into four classes. The attributes acquired from the frontal electrodes, viz., Fp1, Fp2, F3, F4, F8 and Fz, have been used for developing a classifier. The four-class subject-independent emotion classification results in the range of 67–83% have been obtained. Using three classifiers, a mid-range accuracy of 85% has been obtained, which is considerably better than existing studies on ERPs.

scholarly journals Symmetry, topology and the maximum number of mutually pairwise-touching infinite cylinders: configuration classification

2017 ◽  
Vol 4 (1) ◽  
pp. 160729
Author(s):  
Peter V. Pikhitsa ◽  
Stanislaw Pikhitsa
Keyword(s):  
Cross Sections ◽  
Adjacency Matrix ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Classification ◽  
Three Dimensions ◽  
Theory Of Graphs ◽  
Three Dimensional Space

We provide a complete classification of possible configurations of mutually pairwise-touching infinite cylinders in Euclidian three-dimensional space. It turns out that there is a maximum number of such cylinders possible in three dimensions independently of the shape of the cylinder cross-sections. We give the explanation of the uniqueness of the non-trivial configuration of seven equal mutually touching round infinite cylinders found earlier. Some results obtained for the chirality matrix, which is equivalent to the Seidel adjacency matrix, may be found useful for the theory of graphs.

Isomerism and topicity in three- and four-dimensional space: A review

1988 ◽  
Vol 53 (11) ◽  
pp. 2675-2713 ◽  
Author(s):  
Jaroslav Jonas
Keyword(s):  
Dimensional Space ◽  
Rapid Development ◽  
Three Dimensional ◽  
Point Of View ◽  
Molecular Structures ◽  
New Findings ◽  
Chemical Behaviour ◽  
Broad Meaning ◽  
Three Dimensional Space

Isomerism is a notion of a considerably broad meaning. Not only chemists but also physicists, biologists and philosophers come across it. In the sequel, some basic problems of the contemporary understanding of the phenomenon of isomerism of molecular structures and related problems of topic relationships between homomorphic ligands and faces are dealt with. Illustrating factual material is selected within the domain of organic chemistry. With the rapid development of nomenclature in this area in mind, the issues are presented from a point of view stressing the unity of historical and logical moments. Problems arising when moving from the analysis of molecular structure models towards the analysis of real sets of molecules are highlighted. Differences between the analysis of static molecular structures in three-dimensional space and the analysis of real dynamic molecular structures in four-dimensional space are dealt with in greater detail. The method of NMR spectroscopy is discussed from this standpoint as an example of the most widespread research tool for investigating intramolecular dynamism at present. Stereo-differentiating reactions are also treated briefly and a suggestion is made to introduce into the teaching of isomerism and topicity a classification of differentiating interactions. The relationships discussed are demonstrated comprehensively using the chemical behaviour of an optically active trisubstituted cycloheptatriene-norcaradiene system as an example and, are also discussed in connection with some new findings concerning actual chiral geometries in some conventionally achiral systems. Attention is paid to didactic presentation of the topic and an attempt is made to show probable trends in future development in this domain.

Kinematic Mappings. Part 1: Classification of Algebraic Motions in the Plane

1981 ◽  
Vol 103 (3) ◽  
pp. 585-591 ◽  
Author(s):  
S. De Sa ◽  
B. Roth
Keyword(s):  
Classification Scheme ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Planar Motion ◽  
Rotation Curves ◽  
Planar Motions ◽  
Three Dimensional Space

A classification scheme is developed for algebraic motions in the plane. The method is based upon the study of curves in a special three dimensional space into which the planar motions are mapped. As an example all possible cubic motions are classified. It is shown that this mapping, originally proposed by Blaschke, is based upon the rotation curves and the rotation angles of the planar motion.

A three-dimensional approach for understanding the spectrum of idiopathic inflammatory demyelinating disorders: importance of the ‘attack-related severity’ axis

2007 ◽  
Vol 13 (2) ◽  
pp. 199-207 ◽  
Author(s):  
T Fukazawa ◽  
S Kikuchi
Keyword(s):  
Multiple Sclerosis ◽  
Clinical Course ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Treatment Strategies ◽  
General Concept ◽  
The Central Nervous System ◽  
Demyelinating Disorders ◽  
Three Dimensional Space

Understanding the spectrum of idiopathic inflammatory demyelinating disorders (IIDD) of the central nervous system is an important issue for accurate diagnosis and advancing research on the pathogenesis as well as treatment strategies, but the nosology and the classification of the IIDD remains confusing. Until now, we have tried to apply each disorder within the spectrum to an adequate co-ordinate on a two-dimensional plane. One axis is clinical course and the other is lesion distribution. We reviewed some disorders of the IIDD spectrum, and our recent findings on the fulminant nature of each attack and the expansion of each lesion, which we called attack-related severity in Japanese multiple sclerosis (MS). From our findings and the literature, attack-related severity appears to be a third important factor, in addition to lesion distribution and clinical course. Introduction of the third axis produces a three-dimensional space for a better understanding of the heterogeneous characteristics of IIDD and ‘MS’ syndrome, and can advance treatment strategies for these disorders. As severe attacks seem to be relatively common in Asians but rare in the west, ethnic-related heterogeneity should be considered in understanding the spectrum of IIDD, and there is an urgent need to develop a common general concept of the spectrum, especially for MS. Multiple Sclerosis 2007; 13: 199–207. http://msj.sagepub.com

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