Search results for: optical eye diagram

Authors: Suad M. Abuzariba, Liang Chen, Saeed Hadjifaradji

Abstract:

To evaluate the optical eye diagram due to polarization-mode dispersion (PMD), polarization-dependent loss (PDL), and chromatic dispersion (CD) for a system of highly mode coupled fiber with lumped section at any given optical pulse sequence we present an analytical modle. We found that with considering PDL and the polarization direction correlation between PMD and PDL, a system with highly mode coupled fiber with lumped section can have either higher or lower Q-factor than a highly mode coupled system with same root mean square PDL/PMD values. Also we noticed that a system of two highly mode coupled fibers connected together is not equivalent to a system of highly mode coupled fiber when fluctuation is considered

Keywords: polarization mode dispersion, polarization dependent loss, chromatic dispersion, optical eye diagram

Procedia PDF Downloads 834

Authors: Ashiq Hussain, Mahwash Hussain, Zeenat Parveen

Abstract:

Now a days the demand for broadband service has increased. Due to which the researchers are trying to find a solution to provide a large amount of service. There is a shortage of bandwidth because of the use of downloading video, voice and data. One of the solutions to overcome this shortage of bandwidth is to provide the communication system with passive optical components. We have increased the data rate in this system. From experimental results we have concluded that the quality factor has increased by adding passive optical networks.

Keywords: WDM-PON, optical fiber, BER, Q-factor, eye diagram

Procedia PDF Downloads 475

Authors: W. J. Fan, B. S. Ma

Abstract:

The many-body effect on band structure and optical gain of n+ doping tensile-strained Ge/GeSiSn quantum wells are investigated by using an 8-band k•p method. Phase diagram of Ge/GeSiSn quantum well is obtained. The E-k dispersion curves, band gap renormalization and optical gain spectra including many-body effect will be calculated and discussed. We find that the k.p method without many-body effect will overestimate the optical gain and transition energy.

Keywords: Si photonics, many-body effect, optical gain, Ge-on-Si, Quantum well

Procedia PDF Downloads 707

Authors: Zeineb Ben Azzouz, Wahiba Ben Abdessalem Karaa

Abstract:

The automated extraction of UML class diagram from natural language requirements is a highly challenging task. Many approaches, frameworks and tools have been presented in this field. Nonetheless, the experiments of these tools have shown that there is no approach that can work best all the time. In this context, we propose a new accurate approach to facilitate the automatic mapping from textual requirements to UML class diagram. Our new approach integrates the best properties of statistical Natural Language Processing (NLP) techniques to reduce ambiguity when analysing natural language requirements text. In addition, our approach follows the best practices defined by conceptual modelling experts to determine some patterns indispensable for the extraction of basic elements and concepts of the class diagram. Once the relevant information of class diagram is captured, a XMI document is generated and imported with a CASE tool to build the corresponding UML class diagram.

Keywords: class diagram, user’s requirements, XMI, software engineering

Procedia PDF Downloads 444

Authors: Chiung-Hui Chen

Abstract:

Diagram and drawing are important ways to communicate and the reproduce of architectural design, Due to the development of information and communication technology, the professional thinking of architecture and interior design are also change rapidly. In development process of design, diagram always play very important role. This study is based on diagram theories, observe and record interaction between man and objects, objects and space, and space and time in a modern nuclear family. Construct a method for diagram to systematically and visualized describe the space plan of a modern nuclear family toward a intelligent design, to assist designer to retrieve information and check/review event pattern of past and present.

Keywords: digital diagram, information model, context aware, data analysis

Procedia PDF Downloads 309

Authors: Manea Viorel, Puscoci Sorin, Stoichescu Dan Alexandru

Abstract:

Free Space Optics (FSO) is an optical telecommunication system that uses laser beam to transmit data at high bit rates via terrestrial atmosphere. This article describes a method to obtain higher bit rates, under unfavorable weather conditions using multiple optical beams, which carry information with low optical power. Optical link quality assessment is given by the attenuation on different weather conditions. The goal of this paper is to compare two transmission techniques: mono and multi beam, both affected by atmospheric attenuation, using OOK and L-PPM modulation. Link availability is evaluated using eye-diagram that provides information about the overall bit error rate of the system.

Keywords: free space optics, wireless optic, laser communication, spatial diversity

Procedia PDF Downloads 483

Authors: Abid Boudiar

Abstract:

We propose a simple model to obtain an exact expression of Tc/(Tc,max) for the temperature-doping phase diagram of superconducting cuprates. We showed that our model predicted most phase diagram scenario. We found the exact special doping points p(opt), p(qcp) and an accurate E(g,max). Some other properties such as the stripes length 100.1°A and the energy gap in cuprates chain
6meV can also be calculated exactly. Another interesting consequence of this simple picture is the new magic numbers and the ability to express everything using a (Tc,p) diagram via the golden ratio.

Keywords: superconducting cuprates, phase, pseudogap, hole doping, strips, golden ratio, soliton

Procedia PDF Downloads 448

Authors: Naoki Ohshima, Ken Kaminishi

Abstract:

Four types of dependencies, which are 'Finish-to-start', 'Finish-to-finish', 'Start-to-start' and 'Start-to-finish (S-F)' as logical relationship are modeled based on the definition by 'the predecessor activity is defined as an activity to come before a dependent activity in a schedule' in PMBOK. However, it is found a self-contradiction in the precedence diagram for S-F relationship by PMBOK. In this paper, author would like to validate logical relationship of S-F by Graph Theory and propose a new interpretation of the precedence diagram for S-F relationship.

Keywords: project time management, sequence activity, start-to-finish relationship, precedence diagram, PMBOK

Procedia PDF Downloads 238

Authors: Ahmed Jedidi, Mesfer Mohammed Alshamrani, Alwi Mohammad A. Bamhdi

Abstract:

Optical performance monitoring and optical network management are essential in building a reliable, high-capacity, and service-differentiation enabled all-optical network. One of the serious problems in this network is the fact that optical crosstalk is additive, and thus the aggregate effect of crosstalk over a whole AON may be more nefarious than a single point of crosstalk. As results, we note a huge degradation of the Quality of Service (QoS) in our network. For that, it is necessary to identify and monitor the impairments in whole network. In this way, this paper presents new system to identify and monitor crosstalk in AONs in real-time fashion. particular, it proposes a new technique to manage intra-crosstalk in objective to relax QoS of the network.

Keywords: all-optical networks, optical crosstalk, optical cross-connect, crosstalk, monitoring crosstalk

Procedia PDF Downloads 426

Authors: Maha Sliti, Walid Abdallah, Noureddine Boudriga

Abstract:

In the frame of this work, we present an optical multicasting approach based on optical code-words. Our approach associates, in the edge node, an optical code-word to a group multicast address. In the core node, a set of tunable decoders are used to send a traffic data to multiple destinations based on the received code-word. The use of code-words, which correspond to the combination of an input port and a set of output ports, allows the implementation of an optical switching matrix. At the reception of a burst, it will be delayed in an optical memory. And, the received optical code-word is split to a set of tunable optical decoders. When it matches a configured code-word, the delayed burst is switched to a set of output ports.

Keywords: optical multicast, optical burst switching networks, optical code-words, tunable decoder, virtual optical memory

Procedia PDF Downloads 573

Authors: Bayu Anggara, Arita Dewi Nugrahini, Didik Purwadi

Abstract:

Dry sorting workstation needs labor to produce green tea in Gambung Tea Factory. Observation results show that there is labor who are not working at the moment and doing overtime jobs to meet production targets. The measurement of the level of labor effectiveness has never been done before. The purpose of this study is to determine the level of labor effectiveness and provide recommendations for improvement based on the results of the Pareto diagram and Ishikawa diagram. The method used to measure the level of labor effectiveness is Overall Labor Effectiveness (OLE). OLE had three indicators which are availability, performance, and quality. Recommendations are made based on the results of the Pareto diagram and Ishikawa diagram for indicators that do not meet world standards. Based on the results of the study, the OLE value was 68.19%. Recommendations given to improve labor performance are adding mechanics, rescheduling rest periods, providing special training for labor, and giving rewards to labor. Furthermore, the recommendations for improving the quality of labor are procuring water content measuring devices, create material standard policies, and rescheduling rest periods.

Keywords: Ishikawa diagram, labor effectiveness, OLE, Pareto diagram

Procedia PDF Downloads 193

Authors: G. R. Kavitha, T. S. Indumathi

Abstract:

With the constantly rising demands of the multimedia services, the requirements of long haul transport network are constantly changing in the area of optical network. Maximum data transmission using optimization of the communication channel poses the biggest challenge. Although there has been a constant focus on this area from the past decade, there was no evidence of a significant result that has been accomplished. Hence, after reviewing some potential design of optical network from literatures, it was understood that optical signal to noise ratio was one of the elementary attributes that can define the performance of the optical network. In this paper, we propose a framework termed as ECON (Enhanced Constraint-based Optical Network) that primarily optimize the optical signal to noise ratio using ROADM. The simulation is performed in Matlab and optical signal to noise ratio is extracted considering the system matrix. The outcome of the proposed study shows that optimized OSNR as compared to the existing studies.

Keywords: component, optical network, reconfigurable optical add-drop multiplexer, optical signal-to-noise ratio

Procedia PDF Downloads 461

Authors: Jihoon Park, Sungkon Yu, Byungjo Jung

Abstract:

Although various optical tissue phantoms (OTPs) simulating human skin have been actively studied, their completeness is unclear because skin tissue has the intricate optical property and complicated structure disturbing the optical simulation. In this study, we designed multilayer OTP mimicking skin structure, and fabricated OTP models simulating skin-blood vessel and skin pigmentation in the skin, which are useful in Biomedical optics filed. The OTPs were characterized with the optical property and the cross-sectional structure, and analyzed by using various optical tools such as a laser speckle imaging system, OCT and a digital microscope to show the practicality. The measured optical property was within 5% error, and the thickness of each layer was uniform within 10% error in micrometer scale.

Keywords: blood vessel, optical tissue phantom, optical property, skin tissue, pigmentation

Procedia PDF Downloads 414

Authors: Leila Graini

Abstract:

In this paper, we demonstrate basic all-optical functions for 2R regeneration (Re-amplification and Re-shaping) based on self-similar spectral broadening in low normal dispersion and highly nonlinear fiber (ND-HNLF) to regenerate the signal through optical filtering including the transfer function characteristics, and output extinction ratio. Our approach of all-optical 2R regeneration is based on those of Mamyshev. The numerical study reveals the self-similar spectral broadening very effective for 2R all-optical regeneration; the proposed design presents high stability compared to a conventional regenerator using SPM broadening with reduction of the intensity fluctuations and improvement of the extinction ratio.

Keywords: all-optical function, 2R optical regeneration, self-similar broadening, Mamyshev regenerator

Procedia PDF Downloads 162

Authors: Satyasen Panda, Urmila Bhanja

Abstract:

In this paper, we have presented and analyzed three-dimensional (3-D) matrices of wavelength/time/space code for optical code division multiple access (OCDMA) networks with NAND subtraction detection technique. The 3-D codes are constructed by integrating a two-dimensional modified quadratic congruence (MQC) code with one-dimensional modified prime (MP) code. The respective encoders and decoders were designed using fiber Bragg gratings and optical delay lines to minimize the bit error rate (BER). The performance analysis of the 3D-OCDMA system is based on measurement of signal to noise ratio (SNR), BER and eye diagram for a different number of simultaneous users. Also, in the analysis, various types of noises and multiple access interference (MAI) effects were considered. The results obtained with NAND detection technique were compared with those obtained with OR and AND subtraction techniques. The comparison results proved that the NAND detection technique with 3-D MQC\MP code can accommodate more number of simultaneous users for longer distances of fiber with minimum BER as compared to OR and AND subtraction techniques. The received optical power is also measured at various levels of BER to analyze the effect of attenuation.

Keywords: Cross Correlation (CC), Three dimensional Optical Code Division Multiple Access (3-D OCDMA), Spectral Amplitude Coding Optical Code Division Multiple Access (SAC-OCDMA), Multiple Access Interference (MAI), Phase Induced Intensity Noise (PIIN), Three Dimensional Modified Quadratic Congruence/Modified Prime (3-D MQC/MP) code

Procedia PDF Downloads 388

Authors: Valentina Alessandra Carvalho do Vale, Elmo Thiago Lins Cöuras Ford

Abstract:

Increasingly telecommunications sectors are adopting optical technologies, due to its ability to transmit large amounts of data over long distances. However, as in all systems of data transmission, optical communication channels suffer from undesirable and non-deterministic effects, being essential to know the same. Thus, this research allows the assessment of these effects, as well as their characterization and beneficial uses of these effects.

Keywords: optical communication, optical fiber, non-deterministic effects, telecommunication

Procedia PDF Downloads 759

Authors: A. Hadj Taieb, H. Ennouri

Abstract:

The current study aimed to investigate the effect that optical illusion garments have on a woman’s self-perception of her own body shape. First, we created different optical illusion garment by using color contrasts. Second, a short survey based on visual perception is addressed to women in order to compare the different optical illusion garments to determine if they met the established 'ideal' body shape. A ‘visual analysis method’ was used to investigate the clothing models with optical illusions. The theories in relation with the optical illusion were used through this method. The effects of the optical illusion of color contrast on body shape in the fashion sector were tried to be revealed.

Keywords: optical illusion, color contrasts, body image perception, self-esteem

Procedia PDF Downloads 249

Authors: Kadam Bhambri, Neena Gupta

Abstract:

All optical wavelength conversion is essential in present day optical networks for transparent interoperability, contention resolution, and wavelength routing. The incorporation of all optical wavelength convertors leads to better utilization of the network resources and hence improves the efficiency of optical networks. Wavelength convertors that can work with Dispersion Managed (DM) solitons are attractive due to their superior transmission capabilities. In this paper, wavelength conversion for dispersion managed soliton signals was demonstrated at 100 Gbps through semiconductor optical amplifier and an optical filter. The wavelength conversion was achieved for a 1550 nm input signal to1555nm output signal. The output signal was measured in terms of BER, Q factor and system margin.    

Keywords: all optical wavelength conversion, dispersion managed solitons, semiconductor optical amplifier, cross gain modultation

Procedia PDF Downloads 420

Authors: Basavaraj Vadavadagi, Satishkumar Shekhawat

Abstract:

Interstitial free steels posses better formability and have many applications in automotive industries. Forming limit diagrams (FLDs) indicate the formability of materials which can be determined by experimental and finite element (FE) simulations. FLDs were determined experimentally by LDH test, utilizing optical strain measurement system for measuring the strains in different width specimens and by FE simulations in Interstitial Free (IF) and Interstitial Free High Strength (IFHS) steels. In this study, the experimental and FE simulated FLDs are compared and also the stress based FLDs were investigated.

Keywords: forming limit diagram, limiting dome height, optical strain measurement, interstitial

Procedia PDF Downloads 200

Authors: Shreyas Srinivas Rangan, Jurgis Porins

Abstract:

The internet traffic has increased exponentially due to the high demand for data rates by the users, and the constantly increasing metro networks and access networks are focused on improving the maximum transmit distance of the long-reach optical networks. One of the common methods to improve the maximum transmit distance of the long-reach optical networks at the component level is to use broadband optical amplifiers. The Erbium Doped Fiber Amplifier (EDFA) provides high amplification with low noise figure but due to the characteristics of EDFA, its operation is limited to C-band and L-band. In contrast, the Raman amplifier exhibits a wide amplification spectrum, and negative noise figure values can be achieved. To obtain such results, high powered pumping sources are required. Operating Raman amplifiers with such high-powered optical sources may cause fire hazards and it may damage the optical system. In this paper, we implement a hybrid optical amplifier configuration. EDFA and Raman amplifiers are used in this hybrid setup to combine the advantages of both EDFA and Raman amplifiers to improve the reach of the system. Using this setup, we analyze the maximum transmit distance of the network by obtaining a correlation diagram between the length of the single-mode fiber (SMF) and the Bit Error Rate (BER). This hybrid amplifier configuration is implemented in a Wavelength Division Multiplexing (WDM) system with a BER of 10⁻⁹ by using NRZ modulation format, and the gain uniformity noise ratio (signal-to-noise ratio (SNR)), the efficiency of the pumping source, and the optical signal gain efficiency of the amplifier are studied experimentally in a mathematical modelling environment. Numerical simulations were implemented in RSoft OptSim simulation software based on the nonlinear Schrödinger equation using the Split-Step method, the Fourier transform, and the Monte Carlo method for estimating BER.

Keywords: Raman amplifier, erbium doped fibre amplifier, bit error rate, hybrid optical amplifiers

Procedia PDF Downloads 33

Authors: C. W. Kan

Abstract:

This study examines the results of optical whitening process of different textiles such as cotton, wool and polyester. The optical whitening agents used are commercially available products, and the optical whitening agents were applied to the textiles with manufacturers’ suggested methods. The aim of this study is to illustrate the proper application methods of optical whitening agent to different textiles and hence to provide guidance note to the students in learning this topic. Acknowledgment: Authors would like to thank the financial support from the Hong Kong Polytechnic University for this work.

Keywords: learning materials, optical whitening agent, wool, cotton, polyester

Procedia PDF Downloads 401

Authors: B. Bouadjemi, S. Bentata, A. Abbad, W.Benstaali

Abstract:

The full-potential linearized augmented plane wave method (FP-LAPW) within the Generalized Gradient Approximation (GGA) is used to calculate the magnetic and optical properties of quaternary GaFeMnN. The results show that the compound becomes magnetic and half metallic and there is an apparition of peaks at low frequencies for the optical properties.

Keywords: optical properties, DFT, Spintronic, wave

Procedia PDF Downloads 524

Authors: Faisal A. Aburub

Abstract:

Organizations today need to invest in software in order to run their businesses, and to the organizations’ objectives, the software should be in line with the business process. This research presents an approach for linking process models and system models. Particularly, the new approach aims to synthesize sequence diagram based on role activity diagram (RAD) model. The approach includes four steps namely: Create business process model using RAD, identify computerized activities, identify entities in sequence diagram and identify messages in sequence diagram. The new approach has been validated using the process of student registration in University of Petra as a case study. Further research is required to validate the new approach using different domains.

Keywords: business process modelling, system models, role activity diagrams, sequence diagrams

Procedia PDF Downloads 352

Authors: Boudene Maamar, Xu Mai

Abstract:

Optical Intersatellite Links (OISLs) are wireless communications using optical signals to interconnect satellites. It is expected to be the next generation wireless communication technology according to its inherent characteristics like: an increased bandwidth, a high data rate, a data transmission security, an immunity to interference, and an unregulated spectrum etc. Optical space links are the best choice for the classical communication schemes due to its distinctive properties; high frequency, small antenna diameter and lowest transmitted power, which are critical factors to define a space communication. This paper discusses the development of free space technology and analyses the parameters and factors to establish a reliable intersatellite links using an optical signal to exchange data between satellites.

Keywords: optical intersatellite links, optical wireless communications, free space optical communications, next generation wireless communication

Procedia PDF Downloads 426

Authors: Shin-Pin Tseng

Abstract:

Nowadays, numerous spectral amplitude coding (SAC) fiber-optic code-division-multiple-access (FO-CDMA) techniques were appealing due to their capable of providing moderate security and relieving the effects of multiuser interference (MUI). Nonetheless, the performance of the previous network is degraded due to fixed in-phase cross-correlation (IPCC) value. Based on the above problems, a new SAC FO-CDMA network using partial M-sequence (PMS) code is presented in this study. Because the proposed PMS code is originated from M-sequence code, the system using the PMS code could effectively suppress the effects of MUI. In addition, two-code keying (TCK) scheme can applied in the proposed SAC FO-CDMA network and enhance the whole network performance. According to the consideration of system flexibility, simple optical encoders/decoders (codecs) using fiber Bragg gratings (FBGs) were also developed. First, we constructed a diagram of the SAC FO-CDMA network, including (N/2-1) optical transmitters, (N/2-1) optical receivers, and one N×N star coupler for broadcasting transmitted optical signals to arrive at the input port of each optical receiver. Note that the parameter N for the PMS code was the code length. In addition, the proposed SAC network was using superluminescent diodes (SLDs) as light sources, which then can save a lot of system cost compared with the other FO-CDMA methods. For the design of each optical transmitter, it is composed of an SLD, one optical switch, and two optical encoders according to assigned PMS codewords. On the other hand, each optical receivers includes a 1 × 2 splitter, two optical decoders, and one balanced photodiode for mitigating the effect of MUI. In order to simplify the next analysis, the some assumptions were used. First, the unipolarized SLD has flat power spectral density (PSD). Second, the received optical power at the input port of each optical receiver is the same. Third, all photodiodes in the proposed network have the same electrical properties. Fourth, transmitting '1' and '0' has an equal probability. Subsequently, by taking the factors of phase‐induced intensity noise (PIIN) and thermal noise, the corresponding performance was displayed and compared with the performance of the previous SAC FO-CDMA networks. From the numerical result, it shows that the proposed network improved about 25% performance than that using other codes at BER=10-9. This is because the effect of PIIN was effectively mitigated and the received power was enhanced by two times. As a result, the SAC FO-CDMA network using PMS codes has an opportunity to apply in applications of the next-generation optical network.

Keywords: spectral amplitude coding, SAC, fiber-optic code-division multiple-access, FO-CDMA, partial M-sequence, PMS code, fiber Bragg grating, FBG

Procedia PDF Downloads 352

Authors: Chi-Lun Liu

Abstract:

Requirements modeling and analysis are important in successful information systems' maintenance. Unified Modeling Language (UML) class diagrams are useful standards for modeling information systems. To our best knowledge, there is a lack of a systems development methodology described by the organism metaphor. The core concept of this metaphor is adaptation. Using the knowledge representation and reasoning approach and ontologies to adopt new requirements are emergent in recent years. This paper proposes an organic methodology which is based on constructivism theory. This methodology is a knowledge representation and reasoning approach to analyze new requirements in the class diagrams maintenance. The process and rules in the proposed methodology automatically analyze inconsistencies in the class diagram. In the big data era, developing an automatic tool based on the proposed methodology to analyze large amounts of class diagram data is an important research topic in the future.

Keywords: knowledge representation, reasoning, ontology, class diagram, software engineering

Procedia PDF Downloads 210

Authors: Wassana Naiyapo, Atichat Sangtong

Abstract:

The processes in software development by Object Oriented methodology have many stages those take time and high cost. The inconceivable error in system analysis process will affect to the design and the implementation process. The unexpected output causes the reason why we need to revise the previous process. The more rollback of each process takes more expense and delayed time. Therefore, the good test process from the early phase, the implemented software is efficient, reliable and also meet the user’s requirement. Unified Modelling Language (UML) is the tool which uses symbols to describe the work process in Object Oriented Analysis (OOA). This paper presents the approach for automatically generated UML use case diagram and test cases. UML use case diagram is generated from the event table and test cases are generated from use case specifications and Graphic User Interfaces (GUI). Test cases are derived from the Classification Tree Method (CTM) that classify data to a node present in the hierarchy structure. Moreover, this paper refers to the program that generates use case diagram and test cases. As the result, it can reduce work time and increase efficiency work.

Keywords: classification tree method, test case, UML use case diagram, use case specification

Procedia PDF Downloads 134

Authors: H. A. Bentounes, A. Abbad, W. Benstaali

Abstract:

Using first principles calculations based on the density functional theory and local spin density approximation, we investigate optical properties of GaFeMnN quaternary compound. Results show that optical properties confirm that GaFeMnN can be a good candidate in the design of thin film solar cells in the visible and ultraviolet parts of the spectrum, and a good sensor in the infrared

Keywords: GaN, optical absorption, semi-metallic, dielectric function

Procedia PDF Downloads 348

Authors: Chayma Bahar, Chokri Baccouch, Hedi Sakli, Nizar Sakli

Abstract:

Harvesting and transport of optical and radiofrequency signals are a topical subject with multiple challenges. In this paper, we present a Optical RECTENNA system. We propose here a hybrid system solar cell antenna for 5G mobile communications networks. Thus, we propose rectifying circuit. A parametric study is done to follow the influence of load resistance and input power on Optical RECTENNA system performance. Thus, we propose a solar cell antenna structure in the frequency band of future 5G standard in 2.45 GHz bands.

Keywords: antenna, IoT, optical rectenna, solar cell

Procedia PDF Downloads 149

Authors: Michela Quadrini

Abstract:

Chord diagrams occur in mathematics, from the study of RNA to knot theory. They are widely used in theory of knots and links for studying the finite type invariants, whereas in molecular biology one important motivation to study chord diagrams is to deal with the problem of RNA structure prediction. An RNA molecule is a linear polymer, referred to as the backbone, that consists of four types of nucleotides. Each nucleotide is represented by a point, whereas each chord of the diagram stands for one interaction for Watson-Crick base pairs between two nonconsecutive nucleotides. A chord diagram is an oriented circle with a set of n pairs of distinct points, considered up to orientation preserving diffeomorphisms of the circle. A linear chord diagram (LCD) is a special kind of graph obtained cutting the oriented circle of a chord diagram. It consists of a line segment, called its backbone, to which are attached a number of chords with distinct endpoints. There is a natural fattening on any linear chord diagram; the backbone lies on the real axis, while all the chords are in the upper half-plane. Each linear chord diagram has a natural genus of its associated surface. To each chord diagram and linear chord diagram, it is possible to associate the intersection graph. It consists of a graph whose vertices correspond to the chords of the diagram, whereas the chord intersections are represented by a connection between the vertices. Such intersection graph carries a lot of information about the diagram. Our goal is to define an LCD equivalence class in terms of identity of intersection graphs, from which many chord diagram invariants depend. For studying these invariants, we introduce a new representation of Linear Chord Diagrams based on a set of appropriate topological operators that permits to model LCD in terms of the relations among chords. Such set is composed of: crossing, nesting, and concatenations. The crossing operator is able to generate the whole space of linear chord diagrams, and a multiple context free grammar able to uniquely generate each LDC starting from a linear chord diagram adding a chord for each production of the grammar is defined. In other words, it allows to associate a unique algebraic term to each linear chord diagram, while the remaining operators allow to rewrite the term throughout a set of appropriate rewriting rules. Such rules define an LCD equivalence class in terms of the identity of intersection graphs. Starting from a modelled RNA molecule and the linear chord, some authors proposed a topological classification and folding. Our LCD equivalence class could contribute to the RNA folding problem leading to the definition of an algorithm that calculates the free energy of the molecule more accurately respect to the existing ones. Such LCD equivalence class could be useful to obtain a more accurate estimate of link between the crossing number and the topological genus and to study the relation among other invariants.

Keywords: chord diagrams, linear chord diagram, equivalence class, topological language

Procedia PDF Downloads 174