Natural classification of knots

2006 ◽  
Vol 463 (2078) ◽  
pp. 569-582 ◽  
Author(s):  
Alessandro Flammini ◽  
Andrzej Stasiak
Keyword(s):  
Knot Theory ◽  
Three Dimensional ◽  
Crossing Number ◽  
Topological Domains ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Simple Quantum ◽  
Knot Space ◽  
Writhe Number

The principal objective of the knot theory is to provide a simple way of classifying and ordering all the knot types. Here, we propose a natural classification of knots based on their intrinsic position in the knot space that is defined by the set of knots to which a given knot can be converted by individual intersegmental passages. In addition, we characterize various knots using a set of simple quantum numbers that can be determined upon inspection of minimal crossing diagram of a knot. These numbers include: crossing number; average three-dimensional writhe; number of topological domains; and the average relaxation value.

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.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Phonetic iconicity in the evaluative morphology of a sample of Indo-European, Niger-Congo and Austronesian languages

2010 ◽  
Vol 3 (2) ◽  
pp. 156-180 ◽  
Author(s):  
Renáta Gregová ◽  
Lívia Körtvélyessy ◽  
Július Zimmermann
Keyword(s):  
Three Dimensional ◽  
Sound Symbolism ◽  
Three Dimensional Model ◽  
Austronesian Languages ◽  
Place Of Articulation ◽  
European Languages ◽  
Phonetic Symbolism ◽  
The Individual ◽  
Core Vocabulary

Universals Archive (Universal #1926) indicates a universal tendency for sound symbolism in reference to the expression of diminutives and augmentatives. The research ( Štekauer et al. 2009 ) carried out on European languages has not proved the tendency at all. Therefore, our research was extended to cover three language families – Indo-European, Niger-Congo and Austronesian. A three-step analysis examining different aspects of phonetic symbolism was carried out on a core vocabulary of 35 lexical items. A research sample was selected out of 60 languages. The evaluative markers were analyzed according to both phonetic classification of vowels and consonants and Ultan's and Niewenhuis' conclusions on the dominance of palatal and post-alveolar consonants in diminutive markers. Finally, the data obtained in our sample languages was evaluated by means of a three-dimensional model illustrating the place of articulation of the individual segments.

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.

Research on cargo-loading optimization based on genetic and fuzzy integration

2021 ◽  
Vol 40 (4) ◽  
pp. 8493-8500
Author(s):  
Yanwei Du ◽  
Feng Chen ◽  
Xiaoyi Fan ◽  
Lei Zhang ◽  
Henggang Liang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Three Dimensional ◽  
Distribution Center ◽  
Long Time ◽  
Low Efficiency ◽  
Decision Making Model ◽  
The Mathematical Model ◽  
Loading Scheme

With the increase of the number of loaded goods, the number of optional loading schemes will increase exponentially. It is a long time and low efficiency to determine the loading scheme with experience. Genetic algorithm is a search heuristic algorithm used to solve optimization in the field of computer science artificial intelligence. Genetic algorithm can effectively select the optimal loading scheme but unable to utilize weight and volume capacity of cargo and truck. In this paper, we propose hybrid Genetic and fuzzy logic based cargo-loading decision making model that focus on achieving maximum profit with maximum utilization of weight and volume capacity of cargo and truck. In this paper, first of all, the components of the problem of goods stowage in the distribution center are analyzed systematically, which lays the foundation for the reasonable classification of the problem of goods stowage and the establishment of the mathematical model of the problem of goods stowage. Secondly, the paper abstracts and defines the problem of goods loading in distribution center, establishes the mathematical model for the optimization of single car three-dimensional goods loading, and designs the genetic algorithm for solving the model. Finally, Matlab is used to solve the optimization model of cargo loading, and the good performance of the algorithm is verified by an example. From the performance evaluation analysis, proposed the hybrid system achieve better outcomes than the standard SA model, GA method, and TS strategy.

scholarly journals Automated Three-Dimensional Detection and Shape Classification of Dendritic Spines from Fluorescence Microscopy Images

PLoS ONE ◽  
2008 ◽  
Vol 3 (4) ◽  
pp. e1997 ◽  
Author(s):  
Alfredo Rodriguez ◽  
Douglas B. Ehlenberger ◽  
Dara L. Dickstein ◽  
Patrick R. Hof ◽  
Susan L. Wearne
Keyword(s):  
Fluorescence Microscopy ◽  
Dendritic Spines ◽  
Three Dimensional ◽  
Shape Classification ◽  
Microscopy Images

Hydrogel-Based Bioinks for Three-Dimensional Bioprinting: Patent Analysis

2021 ◽  
Vol 7 (1) ◽  
pp. 3
Author(s):  
Ahmed Fatimi
Keyword(s):  
Tissue Engineering ◽  
Detailed Analysis ◽  
State Of The Art ◽  
Three Dimensional ◽  
Patent Analysis ◽  
The State ◽  
Driving Factors ◽  
3D Bioprinting ◽  
Preparation Methods

There are a variety of hydrogel-based bioinks commonly used in three-dimensional bioprinting. In this study, in the form of patent analysis, the state of the art has been reviewed by introducing what has been patented in relation to hydrogel-based bioinks. Furthermore, a detailed analysis of the patentability of the used hydrogels, their preparation methods and their formulations, as well as the 3D bioprinting process using hydrogels, have been provided by determining publication years, jurisdictions, inventors, applicants, owners, and classifications. The classification of patents reveals that most inventions intended for hydrogels used as materials for prostheses or for coating prostheses are characterized by their function or properties Knowledge clusters and expert driving factors show that biomaterials, tissue engineering, and biofabrication research is concentrated in the most patents.

THREE DIMENSIONAL INTERPRETATION OF GRAVITATIONAL ANOMALIES

Geophysics ◽  
1952 ◽  
Vol 17 (2) ◽  
pp. 344-364 ◽  
Author(s):  
Fraser S. Grant
Keyword(s):  
Gravitational Field ◽  
Mass Distribution ◽  
Three Dimensional ◽  
Relaxation Method ◽  
The Body ◽  
Multipole Moments ◽  
Size And Shape ◽  
Surface Field ◽  
Derivatives Of

A method is developed for determining the approximate size and shape of the three‐dimensional mass distribution that is required to produce a given gravitational field. The first few reduced multipole moments of the distribution are calculated from the derivatives of the surface field, and the approximative structure is determined from the values of these moments and a knowledge of the density contrast between the body and its surroundings. A system of classification of problems by symmetry is introduced and its practical usage discussed. A relaxation method is described which may be used to adjust the initial solution systematically to give agreement over the whole field. A descriptive discussion is appended.

Sign in / Sign up

Export Citation Format

Share Document