DISCRETE KNOTS

2002 ◽  
Vol 11 (08) ◽  
pp. 1307-1321 ◽  
Author(s):  
ERNESTO BRIBIESCA
Keyword(s):  
Finite Length ◽  
Finite Alphabet ◽  
Orthogonal Direction ◽  
Chain Code ◽  
Line Segments ◽  
Direction Change ◽  
Straight Line ◽  
Starting Point ◽  
A Chain

A method for representing knots by means of a chain code is presented. Knots which are digitalized and represented by the orthogonal direction change chain code are called discrete knots. Discrete knots are composed of constant straight-line segments using only orthogonal directions. The chain elements represent the orthogonal direction changes of the constant straight-line segments of the discrete knot. There are only five possible orthogonal direction changes for representing any discrete knot. Thus, this chain code only considers relatives directions changes, which allows us to have a unique knot descriptor invariant under translation and rotation. Also, this knot descriptor may be starting point normalized. Finally, this unique knot descriptor produces a numerical string of finite length over a finite alphabet, allows us the usage of grammatical techniques for discrete-knot analysis. Thus, we present some prime discrete knot detection examples within composite discrete knots.

A METHOD FOR COMPUTING FAMILIES OF DISCRETE KNOTS USING KNOT NUMBERS

2005 ◽  
Vol 14 (04) ◽  
pp. 405-424 ◽  
Author(s):  
ERNESTO BRIBIESCA
Keyword(s):  
Integer Number ◽  
Orthogonal Direction ◽  
Chain Code ◽  
Line Segments ◽  
Families Of Curves ◽  
Straight Line ◽  
Starting Point ◽  
A Chain ◽  
Self Avoiding Walks

A method for generating families of particular 3D curves which differs from random self-avoiding walks is presented. This method is based on a chain code called knot numbers. The knot-number notation describes discrete knots. A discrete knot is the digitalized representation of a knot and is composed of constant orthogonal straight-line segments. The orthogonal direction changes of the contiguous straight-line segments of the knot define the chain elements. There are only five possible orthogonal direction changes for representing any discrete knot. Thus, the chain elements are considered as one base-five integer number (knot number). In this manner, we obtain a unique knot descriptor. This description is invariant under translation, rotation, starting point, and coding direction of the discrete knot.By evaluating all possible combinations of chain elements of curves and considering some restrictions, we obtain interesting families of curves which allow us to find the smallest nontrivial knot. Finally, we present a modest attempt at building the table of minimal discrete knots.

scholarly journals An Algorithm for Generating a Family of Alternating Knots

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Carlos Velarde ◽  
Ernesto Bribiesca ◽  
Wendy Aguilar
Keyword(s):  
Formal Language ◽  
Finite Alphabet ◽  
Compression Efficiency ◽  
Chain Code ◽  
Line Segments ◽  
Cubic Lattice ◽  
Chain Codes ◽  
Straight Line ◽  
The Family ◽  
A Chain

An algorithm for generating a family of alternating knots (which are described by means of a chain code) is presented. The family of alternating knots is represented on the cubic lattice, that is, each alternating knot is composed of constant orthogonal straight-line segments and is described by means of a chain code. This chain code is represented by a numerical string of finite length over a finite alphabet, allowing the usage of formal-language techniques for alternating-knot representation. When an alternating knot is described by a chain, it is possible to obtain its mirroring image in an easy way. Also, we have a compression efficiency for representing alternating knots, because chain codes preserve information and allow a considerable data reduction.

The Research on Pan-Genes of an Object Boundary

2011 ◽  
Vol 65 ◽  
pp. 530-535
Author(s):  
Jun Ying Tian ◽  
Jian Hai Han ◽  
Hong Lin Chen
Keyword(s):  
Binary Image ◽  
Object Boundary ◽  
Chain Code ◽  
Line Segments ◽  
Basic Properties ◽  
Internal Relations ◽  
A Chain ◽  
Regional Boundary

The aim of this paper is to give some researches and instructions of relations between the special shapes of an object boundary and their 8-adjacency chain code strings, characteristics of these chain code strings, internal relations among these chain code strings. These characteristics can be used to identify the region of an object boundary, when necessary, to generate this regional boundary. But this is irrelevant to various operations on image. This function of a chain code string is similar to the roles of genes in biology, is called pan-genes. An object boundary on binary image is considered by many tiny line segments connected with each other. The research on characteristics of chain code strings of line segments is an important segment of recognition and generation of an object boundary. This paper gives characteristics of chain code strings of pan-genes corresponding line segments, relations among these chain code strings, chain code string organization forms of chain code string units of line segments (these units are abbreviated with UL), the effective ways and methods on recognition and generation of line segments. Thus, this paper studies the chain code features of corners and circles. This paper gives a variety forms and features of ULs, shows the effects and methods on recognition and generation of an object boundary, gets basic properties of chain code strings about corners and circles.

Through the Lens of the Adam Narrative: A Re-consideration of Sūrat al-Baqara

2015 ◽  
Vol 17 (2) ◽  
pp. 24-46 ◽  
Author(s):  
M.O. Klar
Keyword(s):  
Present Article ◽  
Dominant Theme ◽  
Starting Point ◽  
Lexical Items ◽  
A Chain

The thesis of a single pillar or axis around which the longer Medinan suras are structured has been highly influential in the field of sura unity, and scholarship on the structure and coherence of Sūrat al-Baqara has tended to work towards charting the progress of a dominant theme throughout the textual blocks that make up the sura. In order to achieve this, scholars have divided the sura into discrete blocks; many have posited a chain of lexical and thematic links from one block to the next; some have concentrated solely on the hinges and borders between these suggested textual blocks. The present article argues that such methods, while often in themselves illuminating, are by their very nature reductive. As such they can result in the oversight of important elements of the sura. From a starting point of the Adam pericope provided in Q. 2:30–9, this study will focus on the recurrence of a number of its lexical items throughout Sūrat al-Baqara. By methodically tracing the passage of repeated, loosely Fall-related, vocabulary, it will attempt to widen the contextual lens through which the sura's textual blocks are viewed, and establish a broader perspective on its coherence. Via a discussion of the themes of ‘gardens’, ‘parable’, ‘prostration’, ‘covenant’, ‘wrongdoing’ and finally ‘blindness’, this article will posit ‘garments’, not as a structural pillar, but as a pivot around which many of the repeated lexical items of the sura rotate.

ENCRYPTION-DECRYPTION TECHNIQUES FOR PICTURES

1989 ◽  
Vol 03 (03n04) ◽  
pp. 497-503
Author(s):  
RANI SIROMONEY ◽  
K. G. SUBRAMANIAN ◽  
P. J. ABISHA
Keyword(s):  
Public Key ◽  
Two Dimensional ◽  
Chain Code ◽  
Dimensional Array ◽  
Public Key Cryptosystems ◽  
Encryption Decryption ◽  
A Chain

Language theoretic public key cryptosystems for strings and pictures are discussed. Two methods of constructing public key cryptosystems for the safe transmission or storage of chain code pictures are presented; the first one encrypts a chain code picture as a string and the second one as a two-dimensional array.

scholarly journals XXIII.—On the Disruptive Discharge of Electricity: An Experimental Thesis for the Degree of Doctor of Science, Department A

1878 ◽  
Vol 28 (2) ◽  
pp. 633-671 ◽  
Author(s):  
Alexander Macfarlane
Keyword(s):  
Copper Wire ◽  
Late Summer ◽  
The Other ◽  
Straight Line ◽  
Summer Session ◽  
The Difference ◽  
A Chain ◽  
The One ◽  
Metallic Parts ◽  
The University

The experiments to which I shall refer were carried out in the physical laboratory of the University during the late summer session. I was ably assisted in conducting the experiments by three students of the laboratory,—Messrs H. A. Salvesen, G. M. Connor, and D. E. Stewart. The method which was used of measuring the difference of potential required to produce a disruptive discharge of electricity under given conditions, is that described in a paper communicated to the Royal Society of Edinburgh in 1876 in the names of Mr J. A. Paton, M. A., and myself, and was suggested to me by Professor Tait as a means of attacking the experimental problems mentioned below.The above sketch which I took of the apparatus in situ may facilitate tha description of the method. The receiver of an air-pump, having a rod capable of being moved air-tight up and down through the neck, was attached to one of the conductors of a Holtz machine in such a manner that the conductor of the machine and the rod formed one conducting system. Projecting from the bottom of the receiver was a short metallic rod, forming one conductor with the metallic parts of the air-pump, and by means of a chain with the uninsulated conductor of the Holtz machine. Brass balls and discs of various sizes were made to order, capable of being screwed on to the ends of the rods. On the table, and at a distance of about six feet from the receiver, was a stand supporting two insulated brass balls, the one fixed, the other having one degree of freedom, viz., of moving in a straight line in the plane of the table. The fixed insulated ball A was made one conductor with the insulated conductor of the Holtz and the rod of the receiver, by means of a copper wire insulated with gutta percha, having one end stuck firmly into a hole in the collar of the receiver, and having the other fitted in between the glass stem and the hollow in the ball, by which it fitted on to the stem tightly. A thin wire similarly fitted in between the ball B and its insulating stem connected the ball with the insulated half ring of a divided ring reflecting electrometer.

scholarly journals Use of otoliths to estimate size at sexual maturity in fish

2000 ◽  
Vol 43 (4) ◽  
pp. 437-440 ◽  
Author(s):  
Carlos Sérgio Agostinho
Keyword(s):  
Sexual Maturity ◽  
Line Segments ◽  
Alternative Method ◽  
Straight Line ◽  
Size At Sexual Maturity

The viability of an alternative method for estimating the size at sexual maturity of females of Plagioscion squamosissimus (Perciformes, Sciaenidae) was analyzed. This methodology was used to evaluate the size at sexual maturity in crabs, but has not yet been used for this purpose in fishes. Separation of young and adult fishes by this method is accomplished by iterative adjustment of straight-line segments to the data for length of the otolith and length of the fish. The agreement with the estimate previously obtained by another technique and the possibility of calculating the variance indicates that in some cases, the method analyzed can be used successfully to estimate size at sexual maturity in fish. However, additional studies are necessary to detect possible biases in the method.

A STRUCTURAL APPROACH TO ON-LINE CHARACTER RECOGNITION: SYSTEM DESIGN AND APPLICATIONS

1991 ◽  
Vol 05 (01n02) ◽  
pp. 311-335 ◽  
Author(s):  
FATHALLAH NOUBOUD ◽  
RÉJEAN PLAMONDON
Keyword(s):  
Character Recognition ◽  
Computation Time ◽  
Experimental Tests ◽  
Recognition System ◽  
Structural Approach ◽  
Chain Code ◽  
String Comparison ◽  
Average Computation Time ◽  
On Line ◽  
A Chain

This paper presents a real-time constraint-free handprinted character recognition system based on a structural approach. After the preprocessing operation, a chain code is extracted to represent the character. The classification is based on the use of a processor dedicated to string comparison. The average computation time to recognize a character is about 0.07 seconds. During the learning step, the user can define any set of characters or symbols to be recognized by the system. Thus there are no constraints on the handprinting. The experimental tests show a high degree of accuracy (96%) for writer-dependent applications. Comparisons with other system and methods are discussed. We also present a comparison between the processor used in this system and the Wagner and Fischer algorithm. Finally, we describe some applications of the system.

scholarly journals Partitioning Graph Drawings and Triangulated Simple Polygons into Greedily Routable Regions

2017 ◽  
Vol 27 (01n02) ◽  
pp. 121-158 ◽  
Author(s):  
Martin Nöllenburg ◽  
Roman Prutkin ◽  
Ignaz Rutter
Keyword(s):  
Routing Protocol ◽  
Graph Drawing ◽  
Geographic Routing ◽  
Np Hard ◽  
Line Drawings ◽  
Simple Polygons ◽  
Straight Line ◽  
Starting Point ◽  
Minimum Decomposition ◽  
Geographic Routing Protocol

A greedily routable region (GRR) is a closed subset of [Formula: see text], in which any destination point can be reached from any starting point by always moving in the direction with maximum reduction of the distance to the destination in each point of the path. Recently, Tan and Kermarrec proposed a geographic routing protocol for dense wireless sensor networks based on decomposing the network area into a small number of interior-disjoint GRRs. They showed that minimum decomposition is NP-hard for polygonal regions with holes. We consider minimum GRR decomposition for plane straight-line drawings of graphs. Here, GRRs coincide with self-approaching drawings of trees, a drawing style which has become a popular research topic in graph drawing. We show that minimum decomposition is still NP-hard for graphs with cycles and even for trees, but can be solved optimally for trees in polynomial time, if we allow only certain types of GRR contacts. Additionally, we give a 2-approximation for simple polygons, if a given triangulation has to be respected.

Sign in / Sign up

Export Citation Format

Share Document