Figures of Graph Partitioning by Counting, Sequence and Layer Matrices

Tomescu, Mihaela Aurelia; Jäntschi, Lorentz; Rotaru, Doina Iulia

doi:10.3390/math9121419

Cited by 19 publications

(11 citation statements)

References 75 publications

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“…In the following text, we present the pseudo-code Algorithms 2-4 for our swing up method and the LQR for a low-cost RIP platform. The following algorithms of the different calculations for the RIP case are given based on their writing according to the authors [34]. The experimental results are shown in Figures 12-18.…”

Section: Resultsmentioning

confidence: 99%

Control Theory Application for Swing Up and Stabilisation of Rotating Inverted Pendulum

et al. 2021

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This paper introduces a new scheme for sliding mode control using symmetry principles for a rotating inverted pendulum, with the possibility of extension of this control scheme to other dynamic systems. This was proven for swing up and stabilisation control problems via the new sliding mode control scheme using both simulations and experiments of rotary inverted pendulum (RIP) underactuated systems. According to the Lyapunov theory, a section of the pendulum was compensated with a scale error in the upright position, as the desired trajectory was followed by the pendulum arm section. As the RIP’s dynamic equations were nonlinearly complex and coupled, the complex internal dynamics made the task of controller design difficult. The system control for the pathway of the reference model of the rotational actuator with the application of the sliding mode technique for moving back and forth up the inverted pendulum’s structure, till the arm to reach the linear range round the vertical upright position, was created and tested in an existent device. The stabilisation scheme was switched on in the sliding mode as soon as the arm reached the linear range. A comparison of the stabilisation performance for the same rotating inverted pendulum as discussed by other authors revealed that the proposed controller was more flexible and reliable in terms of the swing up and stabilisation time.

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Section: Resultsmentioning

confidence: 99%

Control Theory Application for Swing Up and Stabilisation of Rotating Inverted Pendulum

et al. 2021

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“…Finally, from the aspect of visualization, a citation network which consists of a large number of patents or publications cannot be visualized easily. Appropriate strategies to filter less important paths and/or nodes and leave the most dominant ones or partition the graph (e.g., [81]) will be very helpful for clearly demonstrating the citations. Moreover, choosing dense-areas which pass specific threshold-value of connectedness will also be feasible.…”

Section: Limitations and Future Possibilitiesmentioning

confidence: 99%

A Novel Analytic Framework of Technology Mining Using the Main Path Analysis and the Decision-Making Trial and Evaluation Laboratory-Based Analytic Network Process

et al. 2021

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Tech mining is an analytical method of technology monitoring that can reveal technology trends in different industries. Patent databases are the major sources for information retrieval by tech mining methods. The majority of the commercially viable research and development results in the world can be found in patents. The time and cost of research and development can greatly be reduced if researchers properly analyze patents of prior arts. Appropriate analyses of patents also help firms avoid patent infringement while simultaneously developing new products or services. The main path analysis is a bibliometric method which can be used to derive the most dominant paths in a citation network of patents or academic works and has widely been adopted in tracing the development trajectory of a specific science or technology. Even though main path analysis can derive patent citation relationships and the weight associated with some specific arc of the citation network, the weights associated with patents and influence relationships among patents can hardly be derived based on methods of main path analysis. However, these influence relationships and weight can be crucial for defining research and development and patent aggregation strategies. Thus, the authors want to propose a novel analytic framework which consists of the Decision-Making Trial and Evaluation Laboratory (DEMATEL), the DEMATEL based Analytic Network Process (DANP) and the main path analysis. The proposed analytic framework can be used to derive the influence relationships and influence weights associated with the patents in a main path. Empirical cases based on the main path of a published work and the patent mining results of nanowire field effect transistors from the database of the United States Patent and Trademark Office will be used to demonstrate the feasibility of the proposed analytic framework. The analytic results of empirical research can be used as a basis for infringement evaluation, patent designing around and innovation.

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“…It is worth mentioning here that recent research work on graph colorings extends beyond the study of proper colorings. For more details, we refer the reader to [6,7] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Tutte Polynomials and Graph Symmetries

et al. 2022

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The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph. It has been used to prove long-standing conjectures in knot theory. Furthermore, it is related to the Potts and Ising models in statistical physics. The purpose of this paper is to study the interaction between the Tutte polynomial and graph symmetries. More precisely, we prove that if the automorphism group of the graph G contains an element of prime order p, then the coefficients of the Tutte polynomial of G satisfy certain necessary conditions.

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Figures of Graph Partitioning by Counting, Sequence and Layer Matrices

Cited by 19 publications

References 75 publications

Control Theory Application for Swing Up and Stabilisation of Rotating Inverted Pendulum

Control Theory Application for Swing Up and Stabilisation of Rotating Inverted Pendulum

A Novel Analytic Framework of Technology Mining Using the Main Path Analysis and the Decision-Making Trial and Evaluation Laboratory-Based Analytic Network Process

Tutte Polynomials and Graph Symmetries

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