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Academic literature on the topic 'Graphe de code'

Author: Grafiati
Published: 15 February 2025

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Journal articles on the topic "Graphe de code"

1

Azkarate, Igor, Mikel Ayani, Juan Carlos Mugarza, and Luka Eciolaza. "Petri Net-Based Semi-Compiled Code Generation for Programmable Logic Controllers." Applied Sciences 11, no. 15 (2021): 7161. http://dx.doi.org/10.3390/app11157161.

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Industrial discrete event dynamic systems (DEDSs) are commonly modeled by means of Petri nets (PNs). PNs have the capability to model behaviors such as concurrency, synchronization, and resource sharing, compared to a step transition function chart or GRAphe Fonctionnel de Commande Etape Transition (GRAFCET) which is a particular case of a PN. However, there is not an effective systematic way to implement a PN in a programmable logic controller (PLC), and so the implementation of such a controller outside a PLC in some external software that will communicate with the PLC is very common. There have been some attempts to implement PNs within a PLC, but they are dependent on how the logic of places and transitions is programmed for each application. This work proposes a novel application-independent and platform-independent PN implementation methodology. This methodology is a systematic way to implement a PN controller within industrial PLCs. A great portion of the code will be validated automatically prior to PLC implementation. Net structure and marking evolution will be checked on the basis of PN model structural analysis, and only net interpretation will be manually coded and error-prone. Thus, this methodology represents a systematic and semi-compiled PN implementation method. A use case supported by a digital twin (DT) is shown where the automated solution required by a manufacturing system is carried out and executed in two different devices for portability testing, and the scan cycle periods are compared for both approaches.
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2

MÜLLER, T., and J. S. SERENI. "Identifying and Locating–Dominating Codes in (Random) Geometric Networks." Combinatorics, Probability and Computing 18, no. 6 (2009): 925–52. http://dx.doi.org/10.1017/s0963548309990344.

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We model a problem about networks built from wireless devices using identifying and locating–dominating codes in unit disk graphs. It is known that minimizing the size of an identifying code is -complete even for bipartite graphs. First, we improve this result by showing that the problem remains -complete for bipartite planar unit disk graphs. Then, we address the question of the existence of an identifying code for random unit disk graphs. We derive the probability that there exists an identifying code as a function of the radius of the disks, and we find that for all interesting ranges of r this probability is bounded away from one. The results obtained are in sharp contrast to those concerning random graphs in the Erdős–Rényi model. Another well-studied class of codes is that of locating–dominating codes, which are less demanding than identifying codes. A locating–dominating code always exists, but minimizing its size is still -complete in general. We extend this result to our setting by showing that this question remains -complete for arbitrary planar unit disk graphs. Finally, we study the minimum size of such a code in random unit disk graphs, and we prove that with probability tending to one, it is of size (n/r)2/3+o(1) if r ≤ /2−ϵ is chosen such that nr2 → ∞, and of size n1+o(1) if nr2 ≪ lnn.
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3

Hudry, Olivier, Junnila Ville, and Antoine Lobstein. "On Iiro Honkala’s Contributions to Identifying Codes." Fundamenta Informaticae 191, no. 3-4 (2024): 165–96. http://dx.doi.org/10.3233/fi-242178.

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A set C of vertices in a graph G = (V, E) is an identifying code if it is dominating and any two vertices of V are dominated by distinct sets of codewords. This paper presents a survey of Iiro Honkala’s contributions to the study of identifying codes with respect to several aspects: complexity of computing an identifying code, combinatorics in binary Hamming spaces, infinite grids, relationships between identifying codes and usual parameters in graphs, structural properties of graphs admitting identifying codes, and number of optimal identifying codes.
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4

Saenpholphat, Varaporn, and Ping Zhang. "Conditional resolvability in graphs: a survey." International Journal of Mathematics and Mathematical Sciences 2004, no. 38 (2004): 1997–2017. http://dx.doi.org/10.1155/s0161171204311403.

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For an ordered setW={w1,w2,…,wk}of vertices and a vertexvin a connected graphG, the code ofvwith respect toWis thek-vectorcW(v)=(d(v,w1),d(v,w2),…,d(v,wk)), whered(x,y)represents the distance between the verticesxandy. The setWis a resolving set forGif distinct vertices ofGhave distinct codes with respect toW. The minimum cardinality of a resolving set forGis its dimensiondim(G). Many resolving parameters are formed by extending resolving sets to different subjects in graph theory, such as the partition of the vertex set, decomposition and coloring in graphs, or by combining resolving property with another graph-theoretic property such as being connected, independent, or acyclic. In this paper, we survey results and open questions on the resolving parameters defined by imposing an additional constraint on resolving sets, resolving partitions, or resolving decompositions in graphs.
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5

José, Marco, and Gabriel Zamudio. "Symmetrical Properties of Graph Representations of Genetic Codes: From Genotype to Phenotype." Symmetry 10, no. 9 (2018): 388. http://dx.doi.org/10.3390/sym10090388.

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It has long been claimed that the mitochondrial genetic code possesses more symmetries than the Standard Genetic Code (SGC). To test this claim, the symmetrical structure of the SGC is compared with noncanonical genetic codes. We analyzed the symmetries of the graphs of codons and their respective phenotypic graph representation spanned by the RNY (R purines, Y pyrimidines, and N any of them) code, two RNA Extended codes, the SGC, as well as three different mitochondrial genetic codes from yeast, invertebrates, and vertebrates. The symmetry groups of the SGC and their corresponding phenotypic graphs of amino acids expose the evolvability of the SGC. Indeed, the analyzed mitochondrial genetic codes are more symmetrical than the SGC.
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6

Tang, C. S., and Tyng Liu. "The Degree Code—A New Mechanism Identifier." Journal of Mechanical Design 115, no. 3 (1993): 627–30. http://dx.doi.org/10.1115/1.2919236.

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An important step in the structural synthesis of mechanisms requires the identification of isomorphism between the graphs which represents the mechanism topology. Previously used methods for identifying graph isomorphism either yield incorrect results for some cases or their algorithms are computationally inefficient for this application. This paper describes a new isomorphism identification method which is well suited for the automated structural synthesis of mechanisms. This method uses a new and compact mathematical representation for a graph, called the Degree Code, to identify graph isomorphism. Isomorphic graphs have identical Degree Codes; nonisomorphic graphs have distinct Degree Codes. Therefore, by examining the Degree Codes of the graphs, graph isomorphism is easily and correctly identified. This Degree Code algorithm is simpler and more efficient than other methods for identifying isomorphism correctly. In addition, the Degree Code can serve as an effective nomenclature and storage system for graphs or mechanisms. Although this identification scheme was developed specifically for the structural synthesis of mechanisms, it can be applied to any area where graph isomorphism is a critical issue.
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7

Leslie, Martin. "Hypermap-homology quantum codes." International Journal of Quantum Information 12, no. 01 (2014): 1430001. http://dx.doi.org/10.1142/s0219749914300010.

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We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the possibility of developing fast decoders for them. Codes based on the homology of embeddings of graphs, such as Kitaev's toric code, have been discussed widely in the literature and our class of codes generalize these. We use embedded hypergraphs, which are a generalization of graphs that can have edges connected to more than two vertices. We develop theorems and examples of our hypermap-homology codes, especially in the case that we choose a special type of basis in our homology chain complex. In particular the most straightforward generalization of the m × m toric code to hypermap-homology codes gives us a [(3/2)m2, 2, m] code as compared to the toric code which is a [2m2, 2, m] code. Thus we can protect the same amount of quantum information, with the same error-correcting capability, using less physical qubits.
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8

Schlingemann, D. "Stabilizer codes can be realized as graph codes." Quantum Information and Computation 2, no. 4 (2002): 307–23. http://dx.doi.org/10.26421/qic2.4-4.

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We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
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9

Hwang, Yongsoo, and Jun Heo. "On the relation between a graph code and a graph state." Quantum Information and Computation 16, no. 3&4 (2016): 237–50. http://dx.doi.org/10.26421/qic16.3-4-3.

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A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a superposition of logical qubits of the related graph code. By using the relation, we first discuss that a local complementation which has been used for a graph state can be useful for searching locally equivalent stabilizer codes, and second provide a method to find a stabilizer group of a graph code.
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10

Al-Kadhimi, Aymen M., Ammar E. Abdulkareem, and Charalampos C. Tsimenidis. "Performance Enhancement of LDPC Codes Based on Protograph Construction in 5G-NR Standard." Tikrit Journal of Engineering Sciences 30, no. 4 (2023): 1–10. http://dx.doi.org/10.25130/tjes.30.4.1.

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To meet the high throughput demands, the 3rd Generation Partnership Project has specified the low-density parity check (LDPC) codes in the fifth generation-new radio 5G-NR standard with rate and length compatibility and scalability. This paper presents an extensive performance evaluation and enhancement of LPDC using the protograph-based construction defined in the 5G-NR standard. Firstly, the protograph-LDPC with layered offset min-sum (OMS) decoding, polar with successive cancellation list (SCL), and block turbo code are implemented and compared. Puncturing and shortening are applied to maintain block length at 1024 and code rate at 1/2 for all codes for comparison fairness. The results showed that P-LDPC outperforms its counterparts in terms of bit/ frame error rate (BER/ FER) behavior for given signal-to-noise ratios. Then, different P-LDPC settings were realized to study the effects of base graph selection (Graph1 or Graph2), code rate change (1/3 - 2/3), and block lengths increase (260 – 4160 bits). The simulation outcomes proved that BER performed better for lower coding rates or higher block lengths. Furthermore, P-LDPC behavior was examined over a Rayleigh flat-fading channel to achieve a 12.5 dB coding gain at 0.001 BER compared with uncoded transmission.
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