Relevant bibliographies by topics / Stable graph

Academic literature on the topic 'Stable graph'

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Published: 14 March 2023

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Journal articles on the topic "Stable graph"

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Abudayah, Mohammad, and Omar Alomari. "Semi Square Stable Graphs." Mathematics 7, no. 7 (July 3, 2019): 597. http://dx.doi.org/10.3390/math7070597.

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The independent number of a graph G is the cardinality of the maximum independent set of G, denoted by α ( G ) . The independent dominating number is the cardinality of the smallest independent set that dominates all vertices of G. In this paper, we introduce a new class of graphs called semi-square stable for which α ( G 2 ) = i ( G ) . We give a necessary and sufficient condition for a graph to be semi-square stable, and we study when interval graphs are semi-square stable.
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Wu, Pu, Huiqin Jiang, Sakineh Nazari-Moghaddam, Seyed Mahmoud Sheikholeslami, Zehui Shao, and Lutz Volkmann. "Independent Domination Stable Trees and Unicyclic Graphs." Mathematics 7, no. 9 (September 5, 2019): 820. http://dx.doi.org/10.3390/math7090820.

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A set S ⊆ V ( G ) in a graph G is a dominating set if every vertex of G is either in S or adjacent to a vertex of S . A dominating set S is independent if any pair of vertices in S is not adjacent. The minimum cardinality of an independent dominating set on a graph G is called the independent domination number i ( G ) . A graph G is independent domination stable if the independent domination number of G remains unchanged under the removal of any vertex. In this paper, we study the basic properties of independent domination stable graphs, and we characterize all independent domination stable trees and unicyclic graphs. In addition, we establish bounds on the order of independent domination stable trees.
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Kayali, Moe, and Dan Suciu. "Quasi-Stable Coloring for Graph Compression." Proceedings of the VLDB Endowment 16, no. 4 (December 2022): 803–15. http://dx.doi.org/10.14778/3574245.3574264.

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We propose quasi-stable coloring , an approximate version of stable coloring. Stable coloring, also called color refinement, is a well-studied technique in graph theory for classifying vertices, which can be used to build compact, lossless representations of graphs. However, its usefulness is limited due to its reliance on strict symmetries. Real data compresses very poorly using color refinement. We propose the first, to our knowledge, approximate color refinement scheme, which we call quasi-stable coloring. By using approximation, we alleviate the need for strict symmetry, and allow for a tradeoff between the degree of compression and the accuracy of the representation. We study three applications: Linear Programming, Max-Flow, and Betweenness Centrality, and provide theoretical evidence in each case that a quasi-stable coloring can lead to good approximations on the reduced graph. Next, we consider how to compute a maximal quasi-stable coloring: we prove that, in general, this problem is NP-hard, and propose a simple, yet effective algorithm based on heuristics. Finally, we evaluate experimentally the quasi-stable coloring technique on several real graphs and applications, comparing with prior approximation techniques.
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Liu, Ye. "On Chromatic Functors and Stable Partitions of Graphs." Canadian Mathematical Bulletin 60, no. 1 (March 1, 2017): 154–64. http://dx.doi.org/10.4153/cmb-2016-047-3.

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AbstractThe chromatic functor of a simple graph is a functorization of the chromatic polynomial. M. Yoshinaga showed that two ûnite graphs have isomorphic chromatic functors if and only if they have the same chromatic polynomial. The key ingredient in the proof is the use of stable partitions of graphs. The latter is shown to be closely related to chromatic functors. In this note, we further investigate some interesting properties of chromatic functors associated with simple graphs using stable partitions. Our ûrst result is the determination of the group of natural automorphisms of the chromatic functor, which is, in general, a larger group than the automorphism group of the graph. The second result is that the composition of the chromatic functor associated with a ûnite graph restricted to the category FI of ûnite sets and injections with the free functor into the category of complex vector spaces yields a consistent sequence of representations of symmetric groups that is representation stable in the sense of Church–Farb.
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Osztényi, József. "A study of the neighborhood complex of $-stable Kneser graphs." Gradus 8, no. 3 (2021): 179–86. http://dx.doi.org/10.47833/2021.3.csc.006.

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In 1978, Alexander Schrijver defined the stable Kneser graphs as a vertex critical subgraphs of the Kneser graphs. In the early 2000s, Günter M. Ziegler generalized Schrijver’s construction and defined the s-stable Kneser graphs. Thereafter Frédéric Meunier determined the chromatic number of the s-stable Kneser graphs for special cases and formulated a conjecture on the chromatic number of the s-stable Kneser graphs. In this paper we study a generalization of the s-stable Kneser graphs. For some specific values of the parameter we show that the neighborhood complex of < s, t >-stable Kneser graph has the same homotopy type as the (t − 1)-sphere. In particular, this implies that the chromatic number of this graph is t + 1.
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Tolue, Behnaz. "The stable subgroup graph." Boletim da Sociedade Paranaense de Matemática 36, no. 3 (July 1, 2018): 129–39. http://dx.doi.org/10.5269/bspm.v36i3.31678.

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In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1)\cap H_2\neq 1$ or $St_{G}(H_2)\cap H_1\neq 1$. Its planarity is discussed whenever $G$ is an abelian group, $p$-group, nilpotent, supersoluble or soluble group. Finally, the induced subgraph of stable subgroup graph with vertex set whole non-normal subgroups is considered and its planarity is verified for some certain groups.
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Pask, David, Adam Sierakowski, and Aidan Sims. "Structure theory and stable rank for C*-algebras of finite higher-rank graphs." Proceedings of the Edinburgh Mathematical Society 64, no. 4 (October 4, 2021): 822–47. http://dx.doi.org/10.1017/s0013091521000626.

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AbstractWe study the structure and compute the stable rank of $C^{*}$-algebras of finite higher-rank graphs. We completely determine the stable rank of the $C^{*}$-algebra when the $k$-graph either contains no cycle with an entrance or is cofinal. We also determine exactly which finite, locally convex $k$-graphs yield unital stably finite $C^{*}$-algebras. We give several examples to illustrate our results.
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Halevi, Yatir, Itay Kaplan, and Saharon Shelah. "Infinite stable graphs with large chromatic number." Transactions of the American Mathematical Society 375, no. 3 (December 21, 2021): 1767–99. http://dx.doi.org/10.1090/tran/8570.

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We prove that if G = ( V , E ) G=(V,E) is an ω \omega -stable (respectively, superstable) graph with χ ( G ) > ℵ 0 \chi (G)>\aleph _0 (respectively, 2 ℵ 0 2^{\aleph _0} ) then G G contains all the finite subgraphs of the shift graph S h n ( ω ) \mathrm {Sh}_n(\omega ) for some n n . We prove a variant of this theorem for graphs interpretable in stationary stable theories. Furthermore, if G G is ω \omega -stable with U ⁡ ( G ) ≤ 2 \operatorname {U}(G)\leq 2 we prove that n ≤ 2 n\leq 2 suffices.
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Koh, Zhuan Khye, and Laura Sanità. "Stabilizing Weighted Graphs." Mathematics of Operations Research 45, no. 4 (November 2020): 1318–41. http://dx.doi.org/10.1287/moor.2019.1034.

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An edge-weighted graph [Formula: see text] is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in network bargaining games and cooperative matching games, because they characterize instances that admit stable outcomes. We give the first polynomial-time algorithm to find a minimum cardinality subset of vertices whose removal from G yields a stable graph, for any weighted graph G. The algorithm is combinatorial and exploits new structural properties of basic fractional matchings, which are of independent interest. In contrast, we show that the problem of finding a minimum cardinality subset of edges whose removal from a weighted graph G yields a stable graph, does not admit any constant-factor approximation algorithm, unless P = NP. In this setting, we develop an O(Δ)-approximation algorithm for the problem, where Δ is the maximum degree of a node in G.
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Jardine, J. F. "Stable Components and Layers." Canadian Mathematical Bulletin 63, no. 3 (October 23, 2019): 562–76. http://dx.doi.org/10.4153/s000843951900064x.

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AbstractComponent graphs $\unicode[STIX]{x1D6E4}_{0}(F)$ are defined for arrays of sets $F$, and, in particular, for arrays of path components for Vietoris–Rips complexes and Lesnick complexes. The path components of $\unicode[STIX]{x1D6E4}_{0}(F)$ are the stable components of the array $F$. The stable components for the system of Lesnick complexes $\{L_{s,k}(X)\}$ for a finite data set $X$ decompose into layers, which are themselves path components of a graph. Combinatorial scoring functions are defined for layers and stable components.
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Dissertations / Theses on the topic "Stable graph"

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Harris, Elizabeth Marie. "Global Domination Stable Graphs." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/etd/1476.

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A set of vertices S in a graph G is a global dominating set (GDS) of G if S is a dominating set for both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.
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Connelly, Abram. "Numerical evidence for phase transitions of NP-complete problems for instances drawn from Lévy-stable distributions." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2533.

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Random NP-Complete problems have come under study as an important tool used in the analysis of optimization algorithms and help in our understanding of how to properly address issues of computational intractability. In this thesis, the Number Partition Problem and the Hamiltonian Cycle Problem are taken as representative NP-Complete classes. Numerical evidence is presented for a phase transition in the probability of solution when a modified Lévy-Stable distribution is used in instance creation for each. Numerical evidence is presented that show hard random instances exist near the critical threshold for the Hamiltonian Cycle problem. A choice of order parameter for the Number Partition Problem’s phase transition is also given. Finding Hamiltonian Cycles in Erdös-Rényi random graphs is well known to have almost sure polynomial time algorithms, even near the critical threshold. To the author’s knowledge, the graph ensemble presented is the first candidate, without specific graph structure built in, to generate graphs whose Hamiltonicity is intrinsically hard to determine. Random graphs are chosen via their degree sequence generated from a discretized form of Lévy-Stable distributions. Graphs chosen from this distribution still show a phase transition and appear to have a pickup in search cost for the algorithms considered. Search cost is highly dependent on the particular algorithm used and the graph ensemble is presented only as a potential graph ensemble to generate intrinsically hard graphs that are difficult to test for Hamiltonicity. Number Partition Problem instances are created by choosing each element in the list from a modified Lévy-Stable distribution. The Number Partition Problem has no known good approximation algorithms and so only numerical evidence to show the phase transition is provided without considerable focus on pickup in search cost for the solvers used. The failure of current approximation algorithms and potential candidate approximation algorithms are discussed.
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Donato, Karen Ann Ehnot. "The kinetics of a methyl methacrylate polymerization initiated by the stable free radicals in irradiated polytetrafluoroethylene and properties of the resultant graft polymer." Ohio : Ohio University, 1987. http://www.ohiolink.edu/etd/view.cgi?ohiou1171670342.

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Cotté, Grégoire. "d-extensibles, d-bloqueurs et d-transversaux de problèmes d'optimisation combinatoire." Thesis, Paris, CNAM, 2016. http://www.theses.fr/2016CNAM1037/document.

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Dans cette thèse, nous étudions trois catégories de problèmes : les d-extensibles, les d-bloqueurs et les d-transversaux.Les d-extensibles de stables optimaux sont des ensembles de sommets d'un graphe G tels que tout stable de cardinal d du sous-graphe induit par un d-extensible peut être étendu à un stable optimal de G à l'aide de sommets qui n'appartiennent pas au d-extensible. Nous étudions les d-extensibles de cardinal maximal de stables dans les graphes bipartis. Nous démontrons quelques propriétés structurelles puis nous déterminons une borne inférieure du cardinal maximal d'un d-extensible. Nous étudions quelques classes de graphes dans lesquelles déterminer un d-extensible optimal de stables est un problème polynomial. Nous nous intéressons ensuite aux d-extensibles de stables dans les arbres. Nous prouvons plusieurs propriétés structurelles, déterminons une autre borne inférieure du cardinal maximal d'un d-extensible et étudions quelques classes d'arbres dans lesquelles déterminer un d-extensible optimal de stables est un problème polynomial.Les d-bloqueurs de stables sont des ensembles de sommets d'un graphe G tels que, si on retire les sommets d'un d-bloqueur, le cardinal maximal d'un stable du graphe induit par les sommets restants est inférieur d'au moins d au cardinal maximal d'un stable du graphe initial. Nous nous intéressons ici aux d-bloqueurs de coût minimal de stables dans les arbres. Après avoir prouvé une caractérisation des d-bloqueurs de stables dans les arbres, nous démontrons que déterminer un d-bloqueur de coût minimal de stable est un problème polynomial dans une classe d'arbres particulière.Soit Pi un problème d'optimisation sur un ensemble d'éléments fini. Un d-transversal de Pi est un ensembles d'éléments tel que l'intersection entre le d-transversal et toute solution optimale au problème Pi est de cardinal supérieur égal à d. Nous proposons ici une approche de génération de contraintes pour déterminer des d-transversaux de cardinal maximal de problèmes modélisés par des programmes mathématiques en variables binaires. Nous étudions deux variantes de cette approche que nous testons sur des instances de graphes générés aléatoirement pour déterminer des d-transversaux de stables optimaux et des d-transversaux de couplages optimaux
In this thesis, we study three types of problems : the d-extensibles sets, the d-blockers and the d-transversals.In a graph G, a d-extensible set of maximum independent sets is a subset of vertices of G such that every stable set of cardinality d in the subgraph restricted to the d-extensible set can be extented to a maximum stable set of G using only vertices that do not belong to the d-extensible set. We study d-extensible sets of mxaimum cardinality of stable sets in bipartite graphs. We show some structural properties and we determine a lower bound of the maximum cardinality of a d-extensible set. We consider some classes of graph where finding an optimum d-extensible set can be done in polynomial time. Then, we study the d-extensibles sets of stable sets in trees. We prove some properties on the structures of the d-extensibles sets and we determine another lower bound of the maximum cardinality of a d-extensible set. Finaly, we study somme classes of tree where a d-extensible sets of maximum cardinality can be done in polynomial time.In a graph G, a d-blocker is a subset of vertices such that, if removed, a maximum stable set of the resulting subgraph is of cardinality at most the cardinality of a maximum stable set of G minus d. We study d-blocker of minimal cost of stable sets in tree.We prove a caracterisation of d-blockers in tree and we study a particular classe of trees where computing a d-blocker of minimal cost of stable sets can be done in polynomial time.Let Pi be an optimisation problem on a finite set of elements. A d-transversal of Pi is a subset of elements such that the intersection between the d-transversal and every optimal solution of Pi contains at lest d elements. We propose an approach to compute d-transversal of any optimisation problem modelised by mathematical program with binary variables. We use a contraints generation approach. We compare two variations of this approach on randomly generated graph by computing d-transversals of stables sets and d-transversals of matching
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Lagoutte, Aurélie. "Interactions entre les Cliques et les Stables dans un Graphe." Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL1012/document.

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Cette thèse s'intéresse à différents types d'interactions entre les cliques et les stables, deux objets très importants en théorie des graphes, ainsi qu'aux relations entre ces différentes interactions. En premier lieu, nous nous intéressons au problème classique de coloration de graphes, qui peut s'exprimer comme une partition des sommets du graphe en stables. Nous présentons un résultat de coloration pour les graphes sans triangles ni cycles pairs de longueur au moins 6. Dans un deuxième temps, nous prouvons la propriété d'Erdös-Hajnal, qui affirme que la taille maximale d'une clique ou d'un stable devient polynomiale (contre logarithmique dans les graphes aléatoires) dans le cas des graphes sans chemin induit à k sommets ni son complémentaire, quel que soit k.Enfin, un problème moins connu est la Clique-Stable séparation, où l'on cherche un ensemble de coupes permettant de séparer toute clique de tout stable. Cette notion a été introduite par Yannakakis lors de l’étude des formulations étendues du polytope des stables dans un graphe parfait. Il prouve qu’il existe toujours un séparateur Clique-Stable de taille quasi-polynomiale, et se demande si l'on peut se limiter à une taille polynomiale. Göös a récemment fourni une réponse négative, mais la question se pose encore pour des classes de graphes restreintes, en particulier pour les graphes parfaits. Nous prouvons une borne polynomiale pour la Clique-Stable séparation dans les graphes aléatoires et dans plusieurs classes héréditaires, en utilisant notamment des outils communs à l'étude de la conjecture d'Erdös-Hajnal. Nous décrivons également une équivalence entre la Clique-Stable séparation et deux autres problèmes : la conjecture d'Alon-Saks-Seymour généralisée et le Problème Têtu, un problème de Satisfaction de Contraintes
This thesis is concerned with different types of interactions between cliques and stable sets, two very important objects in graph theory, as well as with the connections between these interactions. At first, we study the classical problem of graph coloring, which can be stated in terms of partioning the vertices of the graph into stable sets. We present a coloring result for graphs with no triangle and no induced cycle of even length at least six. Secondly, we study the Erdös-Hajnal property, which asserts that the maximum size of a clique or a stable set is polynomial (instead of logarithmic in random graphs). We prove that the property holds for graphs with no induced path on k vertices and its complement.Then, we study the Clique-Stable Set Separation, which is a less known problem. The question is about the order of magnitude of the number of cuts needed to separate all the cliques from all the stable sets. This notion was introduced by Yannakakis when he studied extended formulations of the stable set polytope in perfect graphs. He proved that a quasi-polynomial number of cuts is always enough, and he asked if a polynomial number of cuts could suffice. Göös has just given a negative answer, but the question is open for restricted classes of graphs, in particular for perfect graphs. We prove that a polynomial number of cuts is enough for random graphs, and in several hereditary classes. To this end, some tools developed in the study of the Erdös-Hajnal property appear to be very helpful. We also establish the equivalence between the Clique-Stable set Separation problem and two other statements: the generalized Alon-Saks-Seymour conjecture and the Stubborn Problem, a Constraint Satisfaction Problem
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Pastor, Lucas. "Coloration, ensemble indépendant et structure de graphe." Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAM071/document.

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Cette thèse traite de la coloration de graphe, de la coloration par liste,d'ensembles indépendants de poids maximum et de la théorie structurelle des graphes.Dans un premier temps, nous fournissons un algorithme s'exécutant en temps polynomial pour le problème de la 4-coloration dans des sous-classes de graphe sans $P_6$. Ces algorithmes se basent sur une compréhension précise de la structure de ces classes de graphes, pour laquelle nous donnons une description complète.Deuxièmement, nous étudions une conjecture portant sur la coloration par liste et prouvons que pour tout graphe parfait sans griffe dont la taille de la plus grande clique est bornée par 4, le nombre chromatique est égal au nombre chromatique par liste. Ce résultat est obtenu en utilisant un théorème de décomposition des graphes parfaits sans griffe, une description structurelle des graphes de base de cette décomposition et le célèbre théorème de Galvin.Ensuite, en utilisant la description structurelle élaborée dans le premier chapitre et en renforçant certains aspects de celle-ci, nous fournissons un algorithme s'exécutant en temps polynomial pour le problème d'indépendant de poids maximum dans des sous-classes de graphe sans $P_6$ et sans $P_7$. Dans le dernier chapitre de ce manuscrit, nous infirmons une conjecture datant de 1999 de De Simone et K"orner sur les graphes normaux. Notre preuve est probabiliste et est obtenue en utilisant les graphes aléatoires
This thesis deals with graph coloring, list-coloring, maximum weightstable set (shortened as MWSS) and structural graph theory.First, we provide polynomial-time algorithms for the 4-coloring problem insubclasses of $P_6$-free graphs. These algorithms rely on a preciseunderstanding of the structure of these classes of graphs for which we give afull description.Secondly, we study the list-coloring conjecture and prove that for anyclaw-free perfect graph with clique number bounded by 4, the chromatic numberand the choice number are equal. This result is obtained by using adecomposition theorem for claw-free perfect graphs, a structural description ofthe basic graphs of this decomposition and by using Galvin's famous theorem.Next by using the structural description given in the first chapter andstrengthening other aspects of this structure, we provide polynomial-timealgorithms for the MWSS problem in subclasses of $P_6$-free and $P_7$-freegraphs.In the last chapter of the manuscript, we disprove a conjecture of De Simoneand K"orner made in 1999 related to normal graphs. Our proof is probabilisticand is obtained by the use of random graphs
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Morsellino, Thomas. "Présentation et étude de quelques problèmes d’algorithmique distribuée." Thesis, Bordeaux 1, 2012. http://www.theses.fr/2012BOR14586/document.

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Nous proposons tout d'abord une étude de plusieurs problèmes de l'algorithmique distribuée. Nous fournissons un modèle formel appliqué aux réseaux de diffusion anonymes. Dans ce modèle, nous caractérisons les graphes dans lesquels il est possible de résoudre l'énumération et l'élection. Cette caractérisation se base sur la notion d'homomorphisme de graphes. Nous proposons deux algorithmes dont la complexité est polynomiale et qui améliorent les complexités exponentielles connues jusqu'à présent. Dans un second temps, nous étudions le problème du calcul de l'état global et nous introduisons la notion de weak snapshot. Nous montrons qu'il existe des solutions pour ce problème dans les réseaux anonymes. Nous présentons plusieurs résultats concernant le calcul de l'état global en liaison avec des applications telles que le calcul de points de reprise, la détection de la terminaison ou encore le calcul d'une cartographie du réseau. Dans un cadre plus pratique, nous présentons la conception, le développement et l'implémentation des algorithmes proposés pour le calcul de l'état global au sein du logiciel de simulation et de visualisation ViSiDiA
In this thesis, we first present a study of several problems in the field of distributed algorithms. We provide a formal model that relies on anonymous networks. In this model, we characterize graphs in which it is possible to solve enumeration and leader election problems. This characterization is based on graph homomorphism. We introduce two algorithms with polynomial complexities that improve existing works with exponential complexities. On the other hand, we study the snapshot problem and we introduce the notion of weak snapshot. We show that there exist solutions for this problem in the context of anonymous networks. We present several results about distributed snapshots that deal with checkpoint and rollback recovery, termination detection or the cartography computation of a network. In a practical aspect, we present the conception, the development process and the implementation of these distributed snapshot algorithms within the simulation and visualization software ViSiDiA
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Wang, Suyi Wang. "Analyzing data with 1D non-linear shapes using topological methods." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524020976023345.

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Passuello, Alberto. "Semidefinite programming in combinatorial optimization with applications to coding theory and geometry." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00948055.

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We apply the semidefinite programming method to obtain a new upper bound on the cardinality of codes made of subspaces of a linear vector space over a finite field. Such codes are of interest in network coding.Next, with the same method, we prove an upper bound on the cardinality of sets avoiding one distance in the Johnson space, which is essentially Schrijver semidefinite program. This bound is used to improve existing results on the measurable chromatic number of the Euclidean space.We build a new hierarchy of semidefinite programs whose optimal values give upper bounds on the independence number of a graph. This hierarchy is based on matrices arising from simplicial complexes. We show some properties that our hierarchy shares with other classical ones. As an example, we show its application to the problem of determining the independence number of Paley graphs.
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Jin, Yan. "Hybrid metaheuristic algorithms for sum coloring and bandwidth coloring." Thesis, Angers, 2015. http://www.theses.fr/2015ANGE0062/document.

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Le problème de somme coloration minimum (MSCP) et le problème de coloration de bande passante (BCP) sont deux généralisations importantes du problème de coloration des sommets classique avec de nombreuses applications dans divers domaines, y compris la conception de circuits imprimés, la planication, l’allocation de ressource, l’affectation de fréquence dans les réseaux mobiles, etc. Les problèmes MSCP et BCP étant NP-difficiles, les heuristiques et métaheuristiques sont souvent utilisées en pratique pour obtenir des solutions de bonne qualité en un temps de calcul acceptable. Cette thèse est consacrée à des métaheuristiques hybrides pour la résolution efcace des problèmes MSCP et BCP. Pour le problème MSCP, nous présentons deux algorithmes mémétiques qui combinent l’évolution d’une population d’individus avec de la recherche locale. Pour le problème BCP, nous proposons un algorithme hybride à base d’apprentissage faisant coopérer une méthode de construction “informée” avec une procédure de recherche locale. Les algorithmes développés sont évalués sur des instances biens connues et se révèlent très compétitifs par rapport à l’état de l’art. Les principaux composants des algorithmes que nous proposons sont également analysés
The minimum sum coloring problem (MSCP) and the bandwidth coloring problem (BCP) are two important generalizations of the classical vertex coloring problem with numerous applications in diverse domains, including VLSI design, scheduling, resource allocation and frequency assignment in mobile networks, etc. Since the MSCP and BCP are NP-hard problems, heuristics and metaheuristics are practical solution methods to obtain high quality solutions in an acceptable computing time. This thesis is dedicated to developing effective hybrid metaheuristic algorithms for the MSCP and BCP. For the MSCP, we present two memetic algorithms which combine population-based evolutionary search and local search. An effective algorithm for maximum independent set is devised for generating initial solutions. For the BCP, we propose a learning-based hybrid search algorithm which follows a cooperative framework between an informed construction procedure and a local search heuristic. The proposed algorithms are evaluated on well-known benchmark instances and show highly competitive performances compared to the current state-of-the-art algorithms from the literature. Furthermore, the key issues of these algorithms are investigated and analyzed
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Books on the topic "Stable graph"

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Stable networks and product graphs. Providence, R.I: American Mathematical Society, 1995.

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1959-, Hrushovski Ehud, and Macpherson Dugald, eds. Stable domination and independence in algebraically closed valued fields. Cambridge: Cambridge University Press, 2008.

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Mikov, Aleksandr. Generalized graphs and grammars. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1013698.

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The textbook deals with ordinary graphs and their generalizations-hypergraphs, hierarchical structures, geometric graphs, random and dynamic graphs. Graph grammars are considered in detail. Meets the requirements of the federal state educational standards of higher education of the latest generation. For master's students studying in the areas of the 02.00.00 group "Computer and Information Sciences", and can also be used in senior bachelor's courses and other areas in the field of computer science and computer engineering.
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Gdanskiy, Nikolay. Fundamentals of the theory and algorithms on graphs. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/978686.

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The textbook describes the main theoretical principles of graph theory, the main tasks to be solved using graph structures, and General methods of their solution and specific algorithms, with estimates of their complexity. I covered a lot of the examples given questions to test knowledge and tasks for independent decisions. Along with the control tasks to verify the theoretical training provided practical assignments to develop programs to study topics of graph theory. Meets the requirements of Federal state educational standards of higher education of the last generation. Designed for undergraduate and graduate programs, studying information technology, for in-depth training in analysis and design of systems of complex structure. Also the guide can be useful to specialists of the IT sphere in the study of algorithmic aspects of graph theory.
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Seslavin, Andrey. Theory of automatic control. Linear, continuous systems. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1014654.

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The textbook presents the basics of the classical theory of automatic control, based on mathematical models of real systems, given in the form of systems of linear differential equations with constant coefficients. Methods based on Laplace and Fourier transforms, stability, controllability, and observability theory, as well as directed graph theory and linear algebra are used. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of higher educational institutions studying in the areas of training and specialties 15.00.00 "Mechanical Engineering", 27.00.00 "Management in technical systems".
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Koldaev, Viktor. Theoretical and methodological aspects of the use of information technologies in education. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1014651.

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The article summarizes the experience of implementing a personality-oriented approach to the formation of a structural and content model of the educational process at the university. The results of the introduction of information technologies and their services in the field of education are presented, as well as the impact of computerization on the quality of education in the framework of the modern educational paradigm. The priority directions of innovative educational strategies of the university are identified and a graph model of the individual educational route of the student is proposed in order to predict the state of the educational system and adopt optimal learning strategies. Meets the requirements of the federal state educational standards of higher education of the latest generation. For graduate students and university teachers in the design of variable models of training in any areas of training and specialties. It will be useful for advanced training on the problems of innovative educational strategies.
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Alekseev, Valeriy. Discrete mathematics. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1172256.

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The textbook is written on the basis of a course of lectures on discrete mathematics given to students of the faculty of computational mathematics and Cybernetics of the Lomonosov Moscow state University. It includes an introduction to such sections of discrete mathematics as Boolean functions, k-valued functions, graphs, codes, automata, and the implementation of Boolean functions by schemes. It can be used for reading the course "Discrete mathematics", as well as for self-study of the basics of discrete mathematics.
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Puhal'skiy, Vitaliy. Introduction to Genetics. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1019851.

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The textbook outlines the cytological foundations of heredity, the regularities of Mendelian genetics, the chromosomal theory of heredity, the basics of molecular genetics and genetic engineering, the patterns of inheritance during distant hybridization, polyplodia and mutagenesis. Special attention is paid to the heterosis and genetics of populations. A significant part of the data is presented in the form of figures, diagrams, graphs and tables that facilitate the understanding of the material presented. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of higher educational institutions studying in agronomic specialties.
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Martynova, Tat'yana, Irina Suponickaya, Yuliya Ageeva, Igor' Gorichev, Ol'ga Koval'chukova, and Boleslavna Svetlana. Inorganic chemistry. ru: INFRA-M Academic Publishing LLC., 2023. http://dx.doi.org/10.12737/1860987.

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A textbook with a laboratory workshop on inorganic chemistry contains voluminous theoretical material presented using tables, graphs and reference schemes. At the end of each chapter, control questions, fifteen variants of individual tasks, tests for self-control, laboratory experiments are offered. In the last chapter, compact diagrams-summaries on the main sections of general chemistry are placed as auxiliary material. The appendix provides the necessary reference data. Meets the requirements of the federal state educational standards of higher education of the latest generation. It is intended for students studying in technical specialties and areas of training, as well as for students of specialized classes.
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Balackiy, Evgeniy, Natal'ya Ekimova, Aleksandr Rudnev, and Aleksandr Gusev. New approaches to modeling economic development. ru: INFRA-M Academic Publishing LLC., 2022. http://dx.doi.org/10.12737/1862597.

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The monograph presents new results of the authors' long-term research on various topical issues of economic development. All the proposed new approaches are given in the broad context of already existing theories and models, as well as illustrated by numerous vivid examples from the history of different countries. Most of the topics covered belong to the category of the most burning social issues of our time, which gives the work an element of scientific "freshness" and discussion. All the fundamental theses are accompanied by the necessary models, equations, formulas, graphs and figures, but in general the material is not overloaded with technical details, which makes it quite accessible to any interested reader. The peculiarity of the monograph is that all its sections are based on the "paradox principle", the essence of which is to formulate the original problem in the most acute form, taking the form of a logical paradox. The range of topics under consideration covers the history of mankind from antiquity to the modern state. For example, why did humanity, which had been vegetating in the Malthusian trap for 10 thousand years, break out of it at the turn of the XVII and XVIII centuries? What is needed so that the economic growth that has begun does not "choke" in a short time and does not degenerate again into prolonged stagnation? How are economic growth and return on capital related? How are income inequality and the country's investment activity related? How to measure and in practice link the dialectical properties of institutions that presuppose order and freedom? Is it possible to diagnose "failures" in the regulatory activities of central banks? How to explain the transcendent technological creativity of Russian researchers and engineers with Russia's systematic technological lag behind Western countries? Does Russia have a chance to join the club of the most developed and prosperous countries in the world and what is needed for this? And much, much more. It is addressed to both professional specialists and everyone interested in modern problems of human development.
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Book chapters on the topic "Stable graph"

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Fleiner, Tamás. "On Stable Matchings and Flows." In Graph Theoretic Concepts in Computer Science, 51–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16926-7_7.

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Müller, Haiko. "On the Stable Degree of Graphs." In Graph-Theoretic Concepts in Computer Science, 148–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34611-8_17.

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Biró, Péter, Walter Kern, Daniël Paulusma, and Péter Wojuteczky. "The Stable Fixtures Problem with Payments." In Graph-Theoretic Concepts in Computer Science, 49–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-53174-7_4.

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Le, Van Bang, and Bert Randerath. "On Stable Cutsets in Line Graphs." In Graph-Theoretic Concepts in Computer Science, 263–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45477-2_24.

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Ganesh, Aadityan, H. V. Vishwa Prakash, Prajakta Nimbhorkar, and Geevarghese Philip. "Disjoint Stable Matchings in Linear Time." In Graph-Theoretic Concepts in Computer Science, 94–105. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86838-3_7.

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Kun, Jeremy, Brian Powers, and Lev Reyzin. "Anti-coordination Games and Stable Graph Colorings." In Algorithmic Game Theory, 122–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-41392-6_11.

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Kahraman, Cengiz, Alexander Bozhenyuk, and Margarita Knyazeva. "Internally Stable Set in Intuitionistic Fuzzy Graph." In Lecture Notes in Networks and Systems, 566–72. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09173-5_65.

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Andrade, Diogo V., Endre Boros, and Vladimir Gurvich. "On Graphs Whose Maximal Cliques and Stable Sets Intersect." In Optimization Problems in Graph Theory, 3–63. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94830-0_2.

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Biró, Péter, Matthijs Bomhoff, Petr A. Golovach, Walter Kern, and Daniël Paulusma. "Solutions for the Stable Roommates Problem with Payments." In Graph-Theoretic Concepts in Computer Science, 69–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34611-8_10.

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Demange, Marc, D. de Werra, J. Monnot, and Vangelis Th Paschos. "Weighted Node Coloring: When Stable Sets Are Expensive." In Graph-Theoretic Concepts in Computer Science, 114–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-36379-3_11.

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Conference papers on the topic "Stable graph"

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Buzmakov, Aleksey, Sergei O. Kuznetsov, and Amedeo Napoli. "Efficient Mining of Subsample-Stable Graph Patterns." In 2017 IEEE International Conference on Data Mining (ICDM). IEEE, 2017. http://dx.doi.org/10.1109/icdm.2017.88.

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Hu, Minyang, Hong Chang, Bingpeng Ma, and Shiguang Shan. "Learning Continuous Graph Structure with Bilevel Programming for Graph Neural Networks." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/424.

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Learning graph structure for graph neural networks (GNNs) is crucial to facilitate the GNN-based downstream learning tasks. It is challenging due to the non-differentiable discrete graph structure and lack of ground-truth. In this paper, we address these problems and propose a novel graph structure learning framework for GNNs. Firstly, we directly model the continuous graph structure with dual-normalization, which implicitly imposes sparse constraint and reduces the influence of noisy edges. Secondly, we formulate the whole training process as a bilevel programming problem, where the inner objective is to optimize the GNNs given learned graphs, while the outer objective is to optimize the graph structure to minimize the generalization error of downstream task. Moreover, for bilevel optimization, we propose an improved Neumann-IFT algorithm to obtain an approximate solution, which is more stable and accurate than existing optimization methods. Besides, it makes the bilevel optimization process memory-efficient and scalable to large graphs. Experiments on node classification and scene graph generation show that our method can outperform related methods, especially with noisy graphs.
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Kamkar, Iman, Sunil Gupta, Cheng Li, Dinh Phung, and Svetha Venkatesh. "Stable clinical prediction using graph support vector machines." In 2016 23rd International Conference on Pattern Recognition (ICPR). IEEE, 2016. http://dx.doi.org/10.1109/icpr.2016.7900148.

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Hu, Nan, Raif Rustamov, and Leonidas Guibas. "Stable and Informative Spectral Signatures for Graph Matching." In 2014 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2014. http://dx.doi.org/10.1109/cvpr.2014.296.

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Cervino, Juan, Luana Ruiz, and Alejandro Ribeiro. "Training Stable Graph Neural Networks Through Constrained Learning." In ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2022. http://dx.doi.org/10.1109/icassp43922.2022.9746912.

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Gao, Zhan, and Elvin Isufi. "Learning Stable Graph Neural Networks via Spectral Regularization." In 2022 56th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2022. http://dx.doi.org/10.1109/ieeeconf56349.2022.10051821.

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Isufi, Elvin, Andreas Loukas, and Geert Leus. "Autoregressive moving average graph filters a stable distributed implementation." In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. http://dx.doi.org/10.1109/icassp.2017.7952931.

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Kim, Haklin. "On the maximum stable set of a permutation graph." In the 28th annual Southeast regional conference. New York, New York, USA: ACM Press, 1990. http://dx.doi.org/10.1145/98949.99111.

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Leng, Zhiying, Jiaying Chen, Hubert P. H. Shum, Frederick W. B. Li, and Xiaohui Liang. "Stable Hand Pose Estimation under Tremor via Graph Neural Network." In 2021 IEEE Virtual Reality and 3D User Interfaces (VR). IEEE, 2021. http://dx.doi.org/10.1109/vr50410.2021.00044.

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Jiang, Aimin, Beilu Ni, Jiaan Wan, and Hon Keung Kwan. "Stable ARMA Graph Filter Design via Partial Second-Order Factorization." In 2019 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2019. http://dx.doi.org/10.1109/iscas.2019.8702252.

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Reports on the topic "Stable graph"

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Moeller, Daniel, Ramamohan Paturi, and Moshe Hoffman. Jealousy Graphs: Structure and Complexity of Decentralized Stable Matching. Fort Belvoir, VA: Defense Technical Information Center, January 2013. http://dx.doi.org/10.21236/ada600700.

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Gallagher, B. The State of the Art in Graph-Based Pattern Matching. Office of Scientific and Technical Information (OSTI), March 2006. http://dx.doi.org/10.2172/895418.

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Qi, Fei, Zhaohui Xia, Gaoyang Tang, Hang Yang, Yu Song, Guangrui Qian, Xiong An, Chunhuan Lin, and Guangming Shi. A Graph-based Evolutionary Algorithm for Automated Machine Learning. Web of Open Science, December 2020. http://dx.doi.org/10.37686/ser.v1i2.77.

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As an emerging field, Automated Machine Learning (AutoML) aims to reduce or eliminate manual operations that require expertise in machine learning. In this paper, a graph-based architecture is employed to represent flexible combinations of ML models, which provides a large searching space compared to tree-based and stacking-based architectures. Based on this, an evolutionary algorithm is proposed to search for the best architecture, where the mutation and heredity operators are the key for architecture evolution. With Bayesian hyper-parameter optimization, the proposed approach can automate the workflow of machine learning. On the PMLB dataset, the proposed approach shows the state-of-the-art performance compared with TPOT, Autostacker, and auto-sklearn. Some of the optimized models are with complex structures which are difficult to obtain in manual design.
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Striuk, Andrii, Olena Rybalchenko, and Svitlana Bilashenko. Development and Using of a Virtual Laboratory to Study the Graph Algorithms for Bachelors of Software Engineering. [б. в.], November 2020. http://dx.doi.org/10.31812/123456789/4462.

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The paper presents an analysis of the importance of studying graph algorithms, the reasons for the need to implement this project and its subsequent use. The existing analogues analysis is carried out, due to which a list of advantages and disadvantages is formed and taken into account in developing the virtual laboratory. A web application is created that clearly illustrates the work of graph algorithms, such as Depth-First Search, Dijkstra’s Shortest Path, Floyd- Warshall, Kruskal Minimum Cost Spanning Tree Algorithm. A simple and user- friendly interface is developed and it is supported by all popular browsers. The software product is provided with user registration and authorization functions, chat communication, personal cabinet editing and viewing the statistics on web- application use. An additional condition is taken into account at the design stage, namely the flexibility of the architecture, which envisaged the possibility of easy expansion of an existing functionality. Virtual laboratory is used at Kryvyi Rih National University to training students of specialty 121 Software Engineering in the disciplines “Algorithms and Data Structures” and “Discrete Structures”.
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Nieto-Castanon, Alfonso. CONN functional connectivity toolbox (RRID:SCR_009550), Version 18. Hilbert Press, 2018. http://dx.doi.org/10.56441/hilbertpress.1818.9585.

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CONN is a Matlab-based cross-platform software for the computation, display, and analysis of functional connectivity in fMRI (fcMRI). Connectivity measures include seed-to-voxel connectivity maps, ROI-to- ROI connectivity matrices, graph properties of connectivity networks, generalized psychophysiological interaction models (gPPI), intrinsic connectivity, local correlation and other voxel-to-voxel measures, independent component analyses (ICA), and dynamic component analyses (dyn-ICA). CONN is available for resting state data (rsfMRI) as well as task-related designs. It covers the entire pipeline from raw fMRI data to hypothesis testing, including spatial coregistration, ART-based scrubbing, aCompCor strategy for control of physiological and movement confounds, first-level connectivity estimation, and second-level random-effect analyses and hypothesis testing.
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Nieto-Castanon, Alfonso. CONN functional connectivity toolbox (RRID:SCR_009550), Version 20. Hilbert Press, 2020. http://dx.doi.org/10.56441/hilbertpress.2048.3738.

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CONN is a Matlab-based cross-platform software for the computation, display, and analysis of functional connectivity in fMRI (fcMRI). Connectivity measures include seed-to-voxel connectivity maps, ROI-to- ROI connectivity matrices, graph properties of connectivity networks, generalized psychophysiological interaction models (gPPI), intrinsic connectivity, local correlation and other voxel-to-voxel measures, independent component analyses (ICA), and dynamic component analyses (dyn-ICA). CONN is available for resting state data (rsfMRI) as well as task-related designs. It covers the entire pipeline from raw fMRI data to hypothesis testing, including spatial coregistration, ART-based scrubbing, aCompCor strategy for control of physiological and movement confounds, first-level connectivity estimation, and second-level random-effect analyses and hypothesis testing.
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Nieto-Castanon, Alfonso. CONN functional connectivity toolbox (RRID:SCR_009550), Version 19. Hilbert Press, 2019. http://dx.doi.org/10.56441/hilbertpress.1927.9364.

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CONN is a Matlab-based cross-platform software for the computation, display, and analysis of functional connectivity in fMRI (fcMRI). Connectivity measures include seed-to-voxel connectivity maps, ROI-to- ROI connectivity matrices, graph properties of connectivity networks, generalized psychophysiological interaction models (gPPI), intrinsic connectivity, local correlation and other voxel-to-voxel measures, independent component analyses (ICA), and dynamic component analyses (dyn-ICA). CONN is available for resting state data (rsfMRI) as well as task-related designs. It covers the entire pipeline from raw fMRI data to hypothesis testing, including spatial coregistration, ART-based scrubbing, aCompCor strategy for control of physiological and movement confounds, first-level connectivity estimation, and second-level random-effect analyses and hypothesis testing.
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Mikhaleva, E., E. Babikova, G. Bezhashvili, M. Ilina, and I. Samkova. VALUE STREAM PROGRAM. Sverdlovsk Regional Medical College, December 2022. http://dx.doi.org/10.12731/er0618.03122022.

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In order to increase the efficiency of the work of a medical organization, it is necessary to train medical workers, employees of medical organizations, students of educational organizations in the techniques and methods of lean production, followed by the application of the acquired skills directly at the workplace in a medical organization. The purpose of the training under the program is to acquire new competencies necessary to perform professional tasks using lean manufacturing tools - mapping the value stream to ensure maximum operational efficiency of production processes. The program provides for independent work: mapping the value stream of the current, ideal and target states of the process, analysis of the value stream of the current state of the process (problem identification: spaghetti method, pyramid of problems, graph-links, summary table of root causes and contribution of the solution), development of a plan measures to achieve the target state of the process.
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Соловйов, В. М., and В. В. Соловйова. Моделювання мультиплексних мереж. Видавець Ткачук О.В., 2016. http://dx.doi.org/10.31812/0564/1253.

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From the standpoint of interdisciplinary self-organization theories and synergetics analyzes current approaches to modeling socio-economic systems. It is shown that the complex network paradigm is the foundation on which to build predictive models of complex systems. We consider two algorithms to transform time series or a set of time series to the network: recurrent and graph visibility. For the received network designed dynamic spectral, topological and multiplex measures of complexity. For example, the daily values the stock indices show that most of the complexity measures behaving in a characteristic way in time periods that characterize the different phases of the behavior and state of the stock market. This fact encouraged to use monitoring and prediction of critical and crisis states in socio-economic systems.
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Shah, Ayesha, Jan Olek, and Rebecca S. McDaniel. Real Life Experience with Major Pavement Types. Purdue University, 2022. http://dx.doi.org/10.5703/1288284317371.

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Pavement performance is a complex issue which depends on many contributing factors. Examining the performance of real-life pavements across the state determines what the actual service lives are for the pavements. For the purposes of this study, only selected LTPP projects were examined, along with a database containing all the historic repair projects completed in Indiana. Pertinent information present in the Indiana Historic Contracts Database was extracted concerning the types of pavement repair and treatments options commonly employed within the state, the time between repairs, etc. These data were used to determine descriptive statistical parameters and was summarized in graph form. Similarly, data about selected LTPP GPS and SPS sites were downloaded from the online website, LTPP InfoPave and a comparative study between companion sites was performed. These data included study site and pavement-related information, such as construction dates, pavement structure details, maintenance and repair history, and pavement distress surveys. These data were used to draw conclusions about the impact of treatment applications, climatic and geologic factors, traffic volume, and pavement structures on pavement performance. Gaps in knowledge about pavement failure modes, distress data, and effectiveness of treatment applications mentioned in the contracts database file hampered efforts to form a complete picture of the effectiveness of treatment options and their timely (or untimely) application. Similarly, details about pavement mixture design and differentiating factors between companion sites prevented researchers from narrowing down the causes leading to the observed pavement distress.
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