Journal articles: 'Interval digraphs'

1

Feder, Tomás, Pavol Hell, Jing Huang, and Arash Rafiey. "Adjusted Interval Digraphs." Electronic Notes in Discrete Mathematics 32 (March 2009): 83–91. http://dx.doi.org/10.1016/j.endm.2009.02.012.

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2

Das, S., M. Sen, A. B. Roy, and D. B. West. "Interval digraphs: An analogue of interval graphs." Journal of Graph Theory 13, no. 2 (June 1989): 189–202. http://dx.doi.org/10.1002/jgt.3190130206.

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3

Prisner, Erich. "Algorithms for interval catch digraphs." Discrete Applied Mathematics 51, no. 1-2 (June 1994): 147–57. http://dx.doi.org/10.1016/0166-218x(94)90104-x.

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4

West, Douglas B. "Short proofs for interval digraphs." Discrete Mathematics 178, no. 1-3 (January 1998): 287–92. http://dx.doi.org/10.1016/s0012-365x(97)81840-7.

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5

Sen, Malay, P. Talukdar, and Sandip Das. "Chronological orderings of interval digraphs." Discrete Mathematics 306, no. 14 (July 2006): 1601–9. http://dx.doi.org/10.1016/j.disc.2005.11.032.

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6

Prisner, Erich. "A characterization of interval catch digraphs." Discrete Mathematics 73, no. 3 (1989): 285–89. http://dx.doi.org/10.1016/0012-365x(89)90271-9.

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7

Das, Ashok Kumar, Sandip Das, and Malay Sen. "Forbidden substructure for interval digraphs/bigraphs." Discrete Mathematics 339, no. 2 (February 2016): 1028–51. http://dx.doi.org/10.1016/j.disc.2015.10.010.

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8

Müller, Haiko. "Recognizing interval digraphs and interval bigraphs in polynomial time." Discrete Applied Mathematics 78, no. 1-3 (October 1997): 189–205. http://dx.doi.org/10.1016/s0166-218x(97)00027-9.

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9

Feder, Tomás, Pavol Hell, Jing Huang, and Arash Rafiey. "Interval graphs, adjusted interval digraphs, and reflexive list homomorphisms." Discrete Applied Mathematics 160, no. 6 (April 2012): 697–707. http://dx.doi.org/10.1016/j.dam.2011.04.016.

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Takaoka, Asahi. "A recognition algorithm for adjusted interval digraphs." Discrete Applied Mathematics 294 (May 2021): 253–56. http://dx.doi.org/10.1016/j.dam.2021.02.014.

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11

Paul, Sanchita, and Shamik Ghosh. "On some subclasses of interval catch digraphs." Electronic Journal of Graph Theory and Applications 10, no. 1 (March 20, 2022): 157. http://dx.doi.org/10.5614/ejgta.2022.10.1.10.

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12

Hell, Pavol, and Arash Rafiey. "Monotone Proper Interval Digraphs and Min-Max Orderings." SIAM Journal on Discrete Mathematics 26, no. 4 (January 2012): 1576–96. http://dx.doi.org/10.1137/100783844.

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Cho, Han Hyuk, and Suh-Ryung Kim. "A class of acyclic digraphs with interval competition graphs." Discrete Applied Mathematics 148, no. 2 (May 2005): 171–80. http://dx.doi.org/10.1016/j.dam.2005.02.005.

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14

Meng, Deyuan, Mingjun Du, and Yingmin Jia. "Interval Bipartite Consensus of Networked Agents Associated With Signed Digraphs." IEEE Transactions on Automatic Control 61, no. 12 (December 2016): 3755–70. http://dx.doi.org/10.1109/tac.2016.2528539.

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15

Pavlenko, V. A. "Number of digraphs of periodic points of a continuous mapping of an interval into itself." Ukrainian Mathematical Journal 39, no. 5 (1988): 481–86. http://dx.doi.org/10.1007/bf01066460.

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16

Abdulla, Ugur G., Rashad U. Abdulla, Muhammad U. Abdulla, and Naveed H. Iqbal. "Second Minimal Orbits, Sharkovski Ordering and Universality in Chaos." International Journal of Bifurcation and Chaos 27, no. 05 (May 2017): 1730018. http://dx.doi.org/10.1142/s021812741730018x.

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This paper introduces the notion of second minimal [Formula: see text]-periodic orbits of continuous maps on the interval according to whether [Formula: see text] is a successor of the minimal period of the map in the Sharkovski ordering. We pursue the classification of second minimal [Formula: see text]-orbits in terms of cyclic permutations and digraphs. It is proven that there are nine types of second minimal 7-orbits with accuracy up to inverses. The result is applied to the problem of the distribution of periodic windows within the chaotic regime of the bifurcation diagram of the one-parameter family of unimodal maps. It is revealed that by fixing the maximum number of appearances of periodic windows, there is a universal pattern of distribution. In particular, the first appearance of all the orbits is always a minimal orbit, while the second appearance is a second minimal orbit. It is observed that the second appearance of the 7-orbit is a second minimal 7-orbit with a Type 1 digraph. The reason for the relevance of the Type 1 second minimal orbit is the fact that the topological structure of the unimodal map with a single maximum, is equivalent to the structure of the Type 1 piecewise monotonic endomorphism associated with the second minimal 7-orbit. Yet another important report of this paper is the revelation of universal pattern dynamics with respect to an increased number of appearances.

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Talukdar, Malay Sen P., and Sandip Das. "Chronological Orderings of Interval Digraph." Electronic Notes in Discrete Mathematics 15 (May 2003): 182–85. http://dx.doi.org/10.1016/s1571-0653(04)00574-8.

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18

Sen, Malay K., B. K. Sanyal, and Douglas B. West. "Representing digraphs using intervals or circular arcs." Discrete Mathematics 147, no. 1-3 (December 1995): 235–45. http://dx.doi.org/10.1016/0012-365x(94)00167-h.

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19

Sanyal, Barun K., and Malay K. Sen. "New characterizations of digraphs represented by intervals." Journal of Graph Theory 22, no. 4 (August 1996): 297–303. http://dx.doi.org/10.1002/(sici)1097-0118(199608)22:4<297::aid-jgt3>3.0.co;2-g.

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Das, Ashok Kumar, and Ritapa Chakraborty. "Graphs and digraphs represented by intervals and circular arcs." Discrete Applied Mathematics 228 (September 2017): 41–49. http://dx.doi.org/10.1016/j.dam.2016.11.004.

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Tian, Gui-Xian, Ting-Zhu Huang, and Shu-Yu Cui. "The digraphs and inclusion intervals of matrix singular values." Numerical Linear Algebra with Applications 16, no. 8 (August 2009): 677–87. http://dx.doi.org/10.1002/nla.638.

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22

Martins-Ferreira, Nelson. "Internal Categorical Structures and Their Applications." Mathematics 11, no. 3 (January 28, 2023): 660. http://dx.doi.org/10.3390/math11030660.

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While surveying some internal categorical structures and their applications, it is shown that triangulations and internal groupoids can be unified as two different instances of the same common structure, namely a multi-link. A brief survey includes the categories of directed graphs, reflexive graphs, links, multi-links, triangulations, trigraphs, multiplicative graphs, groupoids, pregroupoids, internal categories, kites, directed kites and multiplicative kites. Most concepts are well-known, and all of them have appeared in print at least once. For example, a multiplicative directed kite has been used as a common generalization for an internal category and a pregroupoid. The scope of the notion of centralization for equivalence relations is widened into the context of digraphs while providing a new characterization of internal groupoids.

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23

Li, Jiong-sheng, Kai Yang, and Qing-xue Wang. "Digraphs and Inclusion Intervals of Brualdi-type for Singular Values." Acta Mathematicae Applicatae Sinica, English Series 18, no. 3 (September 2002): 471–76. http://dx.doi.org/10.1007/s102550200047.

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24

Das, S., and M. Sen. "An interval digraph in relation to its associated bipartite graph." Discrete Mathematics 122, no. 1-3 (November 1993): 113–36. http://dx.doi.org/10.1016/0012-365x(93)90290-a.

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25

Hetmańczyk, Mariusz Piotr. "The Reliability Model of AC-Asynchronous Drive Based on the Multilevel Prognosis System Supported by Matrices and Digraphs Methods." Solid State Phenomena 199 (March 2013): 85–90. http://dx.doi.org/10.4028/www.scientific.net/ssp.199.85.

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Author of this article presents an authorship reliability model of a AC-asynchronous drive written in accordance with assumptions of the multilevel prognosis system based on matrices and digraphs methods. Described model take advantage of knowledge gathered from specialists on the basis of their experience. It is worth to stress that parameters of the reliability model of the AC-drive meet the requirements of units utilized in case of distributed drives. Each change of its application range requires a modification of internal parameters, but the functional structure remains without any variations, because presented reliability model has been based on the functional structure. An intention of the author is focused on an elaboration of a collection of reliability models [ of distributed drives components, prepared in accordance with the multilevel system of prognosis based on matrices and digraphs methods. The model has been specified to the level of the independent subsystem. This approach allows the use of this model in the analysis of complex systems, consisting of separated drive subsystems, which meet the requirements of the method. Using multilevel prediction models should be possible in all applications of electric drives, regardless of purpose functions.

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26

Pramanik, Tarasankar, G. Muhiuddin, Abdulaziz M. Alanazi, and Madhumangal Pal. "An Extension of Fuzzy Competition Graph and Its Uses in Manufacturing Industries." Mathematics 8, no. 6 (June 19, 2020): 1008. http://dx.doi.org/10.3390/math8061008.

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Competition graph is a graph which constitutes from a directed graph (digraph) with an edge between two vertices if they have some common preys in the digraph. Moreover, Fuzzy competition graph (briefly, FCG) is the higher extension of the crisp competition graph by assigning fuzzy value to each vertex and edge. Also, Interval-valued FCG (briefly, IVFCG) is another higher extension of fuzzy competition graph by taking each fuzzy value as a sub-interval of the interval [ 0 , 1 ] . This graph arises in many real world systems; one of them is discussed as follows: Each and every species in nature basically needs ecological balance to survive. The existing species depends on one another for food. If there happens any extinction of any species, there must be a crisis of food among those species which depend on that extinct species. The height of food crisis among those species varies according to their ecological status, environment and encompassing atmosphere. So, the prey to prey relationship among the species cannot be assessed exactly. Therefore, the assessment of competition of species is vague or shadowy. Motivated from this idea, in this paper IVFCG is introduced and several properties of IVFCG and its two variants interval-valued fuzzy k-competition graphs (briefly, IVFKCG) and interval-valued fuzzy m-step competition graphs (briefly, IVFMCG) are presented. The work is helpful to assess the strength of competition among competitors in the field of competitive network system. Furthermore, homomorphic and isomorphic properties of IVFCG are also discussed. Finally, an appropriate application of IVFCG in the competition among the production companies in market is presented to highlight the relevance of IVFCG.

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27

Pamplona, Jill Maegan B., and Imelda S. Aniversario. "On the Planarity of a Directed Pathos Total Digraphs of Some Special Arborescence Graphs." European Journal of Pure and Applied Mathematics 15, no. 3 (July 31, 2022): 1331–43. http://dx.doi.org/10.29020/nybg.ejpam.v15i3.4492.

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An arborescence graph is a directed graph in which, for a vertex u called the root, and any other vertex v, there is exactly one directed path from u to v. The directed pathos of an arborescence Ar is defined as a collection of minimum number of arc disjoint open directed paths whose union is Ar. In [6], for an arborescence Ar, a directed pathos total digraph Q = DP T(Ar)has vertex set V (Q) = V (Ar) ∪ A(Ar) ∪ P(Ar), where V (Ar) is the vertex set, A(Ar) is the arc set, and P(Ar) is a directed pathos set of Ar. The arc set A(Q) consists of the following arcs: ab such that a, b ∈ A(Ar) and the head of a coincides with the tail of b; uv such that u, v ∈ V (Ar) and u is adjacent to v; au(ua) such that a ∈ A(Ar) and u ∈ V (Ar) and the head (tail) of a is u; P a such that a ∈ A(Ar) and P ∈ P(Ar) and the arc a lies on the directed path P; PiPj such that Pi, Pj ∈ P(Ar) and it is possible to reach the head of Pj from the tail of Pi through a common vertex, and it is also possible to reach the head of Pi from the tail of Pj .In this paper, the concept of planarity of the directed pathos total digraph (that is, as an acyclic directed graph which can be drawn with non crossing arcs oriented in one direction) is being discussed and applied to a directed pathos total digraph of an arborescence Ar (DP T(Ar)). Further, the internal vertices of these directed pathos total digraph of Ar are cconsidered.Finally, the planarity of an arborescence resulting from the vertex-gluing of two directed paths ispresented and corresponding internal vertex number is obtained.

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ABRAMS, AARON, ERIC BABSON, HENRY LANDAU, ZEPH LANDAU, and JAMES POMMERSHEIM. "Distributions of Order Patterns of Interval Maps." Combinatorics, Probability and Computing 22, no. 3 (March 5, 2013): 319–41. http://dx.doi.org/10.1017/s0963548313000035.

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A permutation σ describing the relative orders of the first n iterates of a point x under a self-map f of the interval I=[0,1] is called an order pattern. For fixed f and n, measuring the points x ∈ I (according to Lebesgue measure) that generate the order pattern σ gives a probability distribution μn(f) on the set of length n permutations. We study the distributions that arise this way for various classes of functions f.Our main results treat the class of measure-preserving functions. We obtain an exact description of the set of realizable distributions in this case: for each n this set is a union of open faces of the polytope of flows on a certain digraph, and a simple combinatorial criterion determines which faces are included. We also show that for general f, apart from an obvious compatibility condition, there is no restriction on the sequence {μn(f)}n=1,2,. . ..In addition, we give a necessary condition for f to have finite exclusion type, that is, for there to be finitely many order patterns that generate all order patterns not realized by f. Using entropy we show that if f is piecewise continuous, piecewise monotone, and either ergodic or with points of arbitrarily high period, then f cannot have finite exclusion type. This generalizes results of S. Elizalde.

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29

Bountourelis, Theologos, and Spyros Reveliotis. "Optimal Node Visitation in Acyclic Stochastic Digraphs with Multi-threaded Traversals and Internal Visitation Requirements." Discrete Event Dynamic Systems 19, no. 3 (February 19, 2009): 347–76. http://dx.doi.org/10.1007/s10626-009-0065-8.

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30

Ceyhan, Elvan. "Domination number of an interval catch digraph family and its use for testing uniformity." Statistics 54, no. 2 (January 29, 2020): 310–39. http://dx.doi.org/10.1080/02331888.2020.1720020.

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31

Gorelov, D. Y., O. O. Ivanova, O. V. Lytvynenko, A. A. Dovbnia, and D. O. Minin. "Study of the possibilities to use keyboard handwriting for the tasks of identifying students in e-learning systems." Radiotekhnika, no. 207 (December 24, 2021): 139–48. http://dx.doi.org/10.30837/rt.2021.4.207.15.

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When using distance education systems, the problem of information security of the educational process arises, which, in addition to external ones, also implies internal threats. One of these threats can be a legitimate user who paid a fraudster to take tests and give visibility to educational activities under his own name. The use of traditional identification methods has two significant drawbacks: firstly, the ambiguity of the identified user, because the identification of the user occurs by the entered pair login-password; secondly, the inability to detect the substitution of an identified user in the process of working with the system. These disadvantages are eliminated by using biometric methods of covert and continuous monitoring. In the first part of the work the different types of control knowledge tests are analyzed. Taking into account the specifics of the use of covert keyboard monitoring algorithms, the following is proposed: 1) to use tests that do not contain answers; 2) use tests after each learning activities in order to form a user’s biometric vector; 3) use tests with numerical answers in order to minimize the analyzed keystroke digraphs. An algorithm for user’s profile formation and its identification is proposed in the second part of the work. Its combine qualitative (distribution of the frequencies of using numeric keys groups, comma-separated keys, “plus” and “minus” keys on the main and additional keyboard units) and quantitative (analysis of statistical properties of keystroke digraphs) approaches. The experimentally obtained estimates of the identification accuracy of the proposed algorithm: FAR=4.64% and FRR=6.25%.

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32

Kozerenko, Sergiy. "More on linear and metric tree maps." Opuscula Mathematica 41, no. 1 (2021): 55–70. http://dx.doi.org/10.7494/opmath.2021.41.1.55.

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We consider linear and metric self-maps on vertex sets of finite combinatorial trees. Linear maps are maps which preserve intervals between pairs of vertices whereas metric maps are maps which do not increase distances between pairs of vertices. We obtain criteria for a given linear or a metric map to be a positive (negative) under some orientation of the edges in a tree, we characterize trees which admit maps with Markov graphs being paths and prove that the converse of any partial functional digraph is isomorphic to a Markov graph for some suitable map on a tree.

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33

Matsveichuk, N. M., Y. N. Sotskov, and F. Werner. "The dominance digraph as a solution to the two-machine flow-shop problem with interval processing times." Optimization 60, no. 12 (December 2011): 1493–517. http://dx.doi.org/10.1080/02331931003657691.

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34

Ceyhan, Elvan. "The distribution of the relative arc density of a family of interval catch digraph based on uniform data." Metrika 75, no. 6 (February 27, 2011): 761–93. http://dx.doi.org/10.1007/s00184-011-0351-y.

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35

Marchenko, S., and O. Ivashchuk. "Control of gas transmission system in non-stationary consumption modes." Journal of Physics: Conference Series 2131, no. 4 (December 1, 2021): 042003. http://dx.doi.org/10.1088/1742-6596/2131/4/042003.

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Abstract The article deals with the issues of modeling and control of the gas transmission system in non-stationary consumption modes. The topology of the gas transmission network is parameterized in the form of a digraph, with weighted vertices representing the vertices-the drains of consumers, the vertices-the sources of suppliers, transit vertices (compressor or gas distribution stations) and arcs indicating the main parameters that affect the throughput of the system. A hierarchical model of gas transportation system management is proposed, where the upper level is the flow diagram of gas transport, and the lower level simulates the physical processes of gas flow in the pipe section. A procedure for dynamic control in non-stationary consumption modes is developed, which is represented as a sequence of transitions between stationary flow schemes according to the criterion of minimizing their mismatch at neighboring time intervals corresponding to the intervals of constancy of consumption requests, which further reduces the energy costs of changing the flow scheme. The practical value of the research results lies in the possibility of their use while dispatching control.

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36

Boesch, F. T., A. Satyanarayana, and C. L. Suffel. "Some Alternate Characterizations of Reliability Domination." Probability in the Engineering and Informational Sciences 4, no. 2 (April 1990): 257–76. http://dx.doi.org/10.1017/s0269964800001571.

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An important problem in reliability theory is to determine the reliability of a system from the reliability of its components. If E is a finite set of components, then certain subsets of E are prescribed to be the operating states of the system. A formation is any collection F of minimal operating states whose union is E. Reliability domination is defined as the total number of odd cardinality formations minus the total number of even cardinality formations. The purpose of this paper is to establish some new results concerning reliability domination. In the special case where the system can be identified with a graph or digraph, these new results lead to some new graph-theoretic properties and to simple proofs of certain known theorems. The pertinent graph-theoretic properties include spanning trees, acyclic orientations, Whitney's broken cycles, and Tutte's internal activity associated with the chromatic polynomial.

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Kusumastuti, Nilamsari, Raventino, and Fransiskus Fran. "The diachromatic number of double star graph." Journal of Physics: Conference Series 2106, no. 1 (November 1, 2021): 012024. http://dx.doi.org/10.1088/1742-6596/2106/1/012024.

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Abstract We are interested in the extension for the concept of complete colouring for oriented graph G → that has been proposed in many different notions by several authors (Edwards, Sopena, and Araujo-Pardo in 2013, 2014, and 2018, respectively). An oriented colouring is complete if for every ordered pair of colours, at least one arc in G → whose endpoints are coloured with these colours. The diachromatic number, dac ( G → ) , is the greatest number of colours in a complete oriented colouring. In this paper, we establish the formula of diachromatic numbers for double star graph, k 1 , n , n → , over all possible orientations on the graph. In particular, if din (u) = 0 (resp. dout(u) = 0)and din (wi ) = 1 (resp. dout (w 1) = 1) for all i, then dac ( k 1 , n , n → ) = ⌊ n ⌋ + 1 , where u is the internal vertex and w i , i ∈ {1,…, n}, is the pendant vertices of the digraph.

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Masrofah, Masrofah, Lolyana Lolyana, Destiani Destiani, and Erni Mustakim. "ANALISIS FAKTOR KESULITAN MEMBACA PESERTA DIDIK DI KELAS RENDAH." Jurnal Kata : Bahasa, Sastra, dan Pembelajarannya 11, no. 1 (2023): 56–65. http://dx.doi.org/10.23960/kata/v11i1.2023.07.

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The issue in this research is that students cannot read, which makes it difficult for teachers to facilitate learning. This study thus intends to investigate and describe the reading-difficulty factors affecting SD Negeri 8 Metro Timur students in lower grades. This research employed a qualitative approach. While students, teachers, and parents of students provided the study's data sources, the study's participants were SD Negeri 8 Metro Timur students in lower grades. In this study, observation, interviews, and documentation were used to collect data. The results of this study indicate that there was difficulty remembering letters, did not know consonant letters, did not know diffron letters, and did not know digraph letters. The factors of reading difficulty were internal, external, environmental, and psychological. The solution given by educators in class is that they took the time to guide students in class by calling students with difficulty reading. Educators used media such as reading books to train students. Educators also worked closely with parents in monitoring the progress of students.

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Zhilyakova, Liudmila. "Single-Threshold Model Resource Network and Its Double-Threshold Modifications." Mathematics 9, no. 12 (June 21, 2021): 1444. http://dx.doi.org/10.3390/math9121444.

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A resource network is a non-classical flow model where the infinitely divisible resource is iteratively distributed among the vertices of a weighted digraph. The model operates in discrete time. The weights of the edges denote their throughputs. The basic model, a standard resource network, has one general characteristic of resource amount—the network threshold value. This value depends on graph topology and weights of edges. This paper briefly outlines the main characteristics of standard resource networks and describes two its modifications. In both non-standard models, the changes concern the rules of receiving the resource by the vertices. The first modification imposes restrictions on the selected vertices’ capacity, preventing them from accumulating resource surpluses. In the second modification, a network with so-called greedy vertices, on the contrary, vertices first accumulate resource themselves and only then begin to give it away. It is noteworthy that completely different changes lead, in general, to the same consequences: the appearance of a second threshold value. At some intervals of resource values in networks, their functioning is described by a homogeneous Markov chain, at others by more complex rules. Transient processes and limit states in networks with different topologies and different operation rules are investigated and described.

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Yandybaeva, Natalya V. "Dynamic model for predicting quality of life indicators in the region." Journal Of Applied Informatics 18, no. 1 (February 10, 2023): 129–43. http://dx.doi.org/10.37791/2687-0649-2023-18-1-129-143.

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An approach to assessing and forecasting indicators of the quality of life of the population in the region based on the concept of system dynamics is presented. A mathematical model has been developed, which is a system of non-linear, non-homogeneous, different-tempo differential equations, which include system variables and external factors. A digraph of causal relationships between system variables and external factors is constructed. As system variables, the model uses indicators of socio-economic development of the region: gross regional product, life expectancy at birth, population size, per capita per capita income, registered unemployment rate, birth rate, share of the population with income below the subsistence level, the weight of organizations using personal computers. The choice of external factors and functional dependencies in the developed model is substantiated. The adequacy of the developed mathematical model was checked using retrospective data and the calculation of the relative error. The interface of the author’s software application “Prognoz_2”, developed in the GUIDE MatLab environment, used to conduct computational experiments, is presented. An example of the practical implementation of the developed approach to assessing the quality of life in the Saratov and Samara regions is considered. The results of the computational experiment on the analysis and prediction of the quality of life on the time interval [2022;2026] years within the framework of the implementation of three scenarios are shown. The values of system variables in 2021 normalized relative to 2010 were used as initial conditions for the calculations. The developed software can be used to form scenarios for the socio-economic development of the region. Models and algorithms can be used as part of an information-advising system for making decisions at various levels of management.

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Annela, Ayu, and Safran Safran. "Analysis of Early Reading Difficulties for Elementary School Students." Scaffolding: Jurnal Pendidikan Islam dan Multikulturalisme 5, no. 2 (July 13, 2023): 466–84. http://dx.doi.org/10.37680/scaffolding.v5i2.3121.

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This study aims to identify and define the beginning reading teaching and learning process. Some factors contributed to students’ first reading challenges and the teacher's strategies for overcoming those issues in grade II SDN 10 Koto Balingka. Eleven children with reading difficulties were identified as part of the study data gathered during the initial observation of the teaching and learning process in the classroom. In the 2023–2024 school year, it was known that several children had trouble starting to read in the second grade of SDN 10 Koto Balingka. This paper utilized a case study methodology and a qualitative technique with a descriptive qualitative design. Interview results served as the study's primary data sources, and secondary data came from research materials like books, notes, school-related information, learning reports, and documentation—specifically, photographs and audio recordings—related to students' understanding exercises. Perceptions, meetings, and documentation are used in the information-gathering processes. The instruments utilized in this study were guidelines for documentation, observation, and interviews. Data reduction, presentation, and conclusion were made in the data analysis step. The findings from this study show 1) The teacher's initial reading learning process emphasizes conjunctions in the form of simple sentences, using spelling and syllable methods. 2) Difficulty factors that hinder students from beginning reading in second grade consist of internal and external factors. Internal factors include students' physical intelligence, interest, and motivation. External factors include family factors and school factors. 3) Provide additional time for students who still have difficulty reading, teach them to read again by learning to read at home, pay more attention to students who still have difficulty reading at first, teach using various methods, and prepare interesting learning materials. Based on the results of this study, it can be concluded that in the teaching and learning process, there are students' difficulties in beginning reading, including (1) Difficulty in pronouncing consonants; (2) It is difficulty reading digraph letters; (3) It is difficult to distinguish similar letters; (4) Eliminating letters when we read words; (5) Difficulty in reading affixed words; (6) Not using punctuation marks; (7) reading haltingly so that there are many errors in reading; and (8) difficulty in understanding the contents of the reading. Difficulty factors that hinder students in beginning reading in grade II at SDN 10 Koto Balingka consist of students' internal and external factors. Internal factors include (1) Physical factors from students; (2) intelligence factors; (3) Interests; and (4) student motivation. External factors from students include (1) family factors and (2) school factors. The solutions given to overcome the difficulties of class II students at SDN 10 Koto Balingka in the beginning reading are: (1) Providing additional time for students who still have difficulty reading at first; (2) Teaching them to read again by learning to read at home; (3) The teacher pays more attention to students who still have difficulty reading at first; (4) Teaching using various methods; and (5) Preparing interesting learning material.

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Krivonosov, M. I., A. V. Varekhina, K. V. Anokhin, and M. V. Ivanchenko. "Associations of neuro-glial network calcium activity with mice movements <i>in vivo</i>." Genes & Cells 18, no. 4 (December 15, 2023): 850–53. http://dx.doi.org/10.17816/gc623434.

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Calcium imaging of nerve activity in the mouse hippocampus provides insights into cell-to-cell interactions [1]. Over time, fluctuations in cellular calcium levels encode distinct brain states during mouse brain imaging. Although synapses connect cells and transmit information, it is challenging to detect the spatiotemporal transmission pathway via calcium imaging of multiple cells due to the complexity of the spatial structure and imaging in a separate focal plane [2]. Reconstruction of the dynamic graph of connections between cells was proposed to overcome this problem. A dynamic graph comprises of individual graphs for each time point. A graph linked to a particular time t is composed of vertices representing cells and edges that depict the transmission of signals between cells at that moment. This paper puts forth 3 approaches for creating networks. The first method considers the overlapping time intervals of calcium events in individual cells [3]. The link is established between the cell with the earlier event and the cell with the later start of the event during the moments when the events occurred simultaneously in separate cells. Alternatively, time intervals between the start of events were taken into account. Potentially connected events that began no later than 2 s were linked, with the edge drawn from the cell depicting the earlier starting event to the second cell. The third technique involved linking sequentially occurring events in distinct cells. The edge is drawn from all active cells at the previous time step to newly activated cells at the subsequent time step. Data analysis is based on an experiment in which a mouse moved along a circular track while the fluorescence of neuronal calcium activity and the mouse’s position were recorded at a frequency of 20 frames per second [4]. A red dot was marked on the mouse’s head to track its position. The reconstructed dynamic graph was compared to the angular coordinate of the mouse on the ring to look for repeating patterns of activity. The racetrack was divided into 20 overlapping sectors, each spanning 36 degrees. The reconstructed networks were then assigned to sectors that aligned with the mouse’s angular position on the track. Next, we estimated the frequency of individual edge repetitions within each network group. Only edges that occurred at least three times were chosen for further analysis. We found repeated activations of various cell pairs that corresponded to clockwise and counterclockwise movement within the same sector. Furthermore, we identified the presence of alternating activation, where activity occurred in the first cell, then the second cell, and then again in the first cell. In addition, we identified complex sequences of 5–6 non-sequential activations, represented as a digraph without cycles, which is typical for single sectors.

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Benali, Akli, Nuno Guiomar, Hugo Gonçalves, Bernardo Mota, Fábio Silva, Paulo M. Fernandes, Carlos Mota, et al. "The Portuguese Large Wildfire Spread database (PT-FireSprd)." Earth System Science Data 15, no. 8 (August 23, 2023): 3791–818. http://dx.doi.org/10.5194/essd-15-3791-2023.

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Abstract. Wildfire behaviour depends on complex interactions between fuels, topography, and weather over a wide range of scales, being important for fire research and management applications. To allow for significant progress towards better fire management, the operational and research communities require detailed open data on observed wildfire behaviour. Here, we present the Portuguese Large Wildfire Spread database (PT-FireSprd) that includes the reconstruction of the spread of 80 large wildfires that occurred in Portugal between 2015 and 2021. It includes a detailed set of fire behaviour descriptors, such as rate of spread (ROS), fire growth rate (FGR), and fire radiative energy (FRE). The wildfires were reconstructed by converging evidence from complementary data sources, such as satellite imagery and products, airborne and ground data collected by fire personnel, and official fire data and information in external reports. We then implemented a digraph-based algorithm to estimate the fire behaviour descriptors and combined it with the Meteosat Second Generation (MSG) Spinning Enhanced Visible and Infrared Imager (SEVIRI) fire radiative power estimates. A total of 1197 ROS and FGR estimates were calculated along with 609 FRE estimates. The extreme fires of 2017 were responsible for the maximum observed values of ROS (8900 m h−1) and FGR (4400 ha h−1). Combining both descriptors, we describe the fire behaviour distribution using six percentile intervals that can be easily communicated to both research and management communities. Analysis of the database showed that burned extent is mostly determined by FGR rather than by ROS. Finally, we explored a practical example to show how the PT-FireSprd database can be used to study the dynamics of individual wildfires and to build robust case studies for training and capacity building. The PT-FireSprd is the first open-access fire progression and behaviour database in Mediterranean Europe, dramatically expanding the extant information. Updating the PT-FireSprd database will require a continuous joint effort by researchers and fire personnel. PT-FireSprd data are publicly available through https://doi.org/10.5281/zenodo.7495506 (Benali et al., 2022) and have large potential to improve current knowledge on wildfire behaviour and to support better decision making.

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Boychuk, V., A. Boychuk, M. Boychuk, and O. Burdyug. "THE ACTION SEQUENCE FORMING METHOD FOR INTELLECTUAL AGENTS." Collection of scientific works of the Military Institute of Kyiv National Taras Shevchenko University, no. 66 (2019): 65–74. http://dx.doi.org/10.17721/2519-481x/2020/66-07.

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The article proposes an approach where the implementation of the formation of sequences of actions of intelligent agents is carried out by analogy with the activities of biological organisms using the mechanism of emotions to dynamically tune the body to perform actions. Thus, the functions of the limbic system are simulated in the organization of movements based on motivational behavior. When planning, first of all, the general condition of the agent is determined. Using the resulting state, a sequence of actions is formed. This approach will make it possible to dynamically reconfigure the sequence and respond to a dangerous situation or to a change in the internal state of the agent. An intelligent agent receives from the sensors and receptors signs of an initial condition, the goal is determined by it, and a sequence of actions is formed. Elements of a sequence of actions are elementary actions. An elementary action is characterized by a set of input parameters for functioning. Signs of the premise correspond to the first action in the sequence, the last action in the sequence is tied to the sign of the goal. The sequence of actions of the agent is represented by a digraph, where the vertices determine the elementary actions, and the edges determine the degree of bond strength between them. The initial conditions correspond to the first action in the sequence, the implementation of the sequence of actions begins with it. Signs of the goal correspond to the last peak in the sequence of actions Link weights change when general state variables are set, which allows you to perform a sequence of actions in real time with dynamic reconfiguration and select sequences of actions that are characteristic of a particular state. The method forms a sequence of actions that is initiated by emotional states and translates it into a sequence of automatic actions based on the achievement of the goal and which in the future will be performed in a normal state. To test the functioning of the method, a agent-work simulator is implemented in the V-REP program environment. The results obtained can be used for intelligent planning based on reinforcements and can be used in the management of agents, work in manufacturing enterprises, military agents, urban traffic flows, logistics systems, and social phenomena.

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Petrushenko, N. "Spatio-temporal combinatorics of resource flows conservation and reduction of risks in conditions of uncertainty of the external environment." System technologies 1, no. 138 (March 30, 2022): 65–78. http://dx.doi.org/10.34185/1562-9945-1-138-2022-06.

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Management of non-structured and weakly structured systems for the impacts of the dy-namic changes is not have a developed methodological basis. Management decisions are made on the basis of stochastic recommendations based on the results of existing experience with ex-trapolation to future trends without taking into account risks and possible faults. It is not neces-sary to introduce a great lack of value and inadequacy of acceptance of solutions, related to a wide range of criteria for assessments, without a wide range of factors, and highly direct indicators. When modeling management in the conditions of uncertainties of the environment, which are constantly changing, a large variety of source data is possible. The development of methods and models to support decision-making in terms of geo-graphically distributed processes is a very complex and non-trivial task. All interactions take place within a territorially distributed system. Such model can be built on a continuous basis, but it cannot be used to analyze spatial areas in real time. To reduce the level of risk and the results of possible losses, it is necessary to carefully study the possible carriers of risk, taking into account their individual characteristics, as well as market participants with the development of their original methods of risk management. The initial information on identifying problems of unstable market development is contained in the ratio of internal and external destabilizing factors. Information as an integral part of doing business plays a key role in reducing the risks that ensure the commercialization of proposals. Decision-making in a complex system is that from the available set of acceptable con-trols, it is necessary to identify several options that are the best. The rule that establishes the advantage in many solutions is the principle of optimality. When solving problems of optimal control as a set of valid alternatives use the combinatorics of acceptable management. An important difference between the construction of mathematical models of complex systems is that the modeling is not above the global function and the allocation of the main parts, and below, with the construction of models of individual processes and lower hierar-chical levels. Larger modules and the system as a whole are modeled on the basis of reasona-ble complexity. Combinatorics is directly related to simulation modeling, when it is impossible to apply mathematical solutions to problems in conditions of uncertainty. A perspective area of analysis and management of development under conditions of un-certainty and ambiguity of the external environment is graph theory using the Ford-Falkerson algorithm. Control under the action of constantly changing environments with the onset of change is solved using the Ford-Falkerson algorithm. The network of possible movements is considered as a connected digraph. In the conditions of global risks it is not necessary to count only on one direction of de-velopment. The sudden emergence of restrictions forces to move to another branch of the network, for which the network provides additional vertical edges with their probabilities and bandwidth. As the change of the situation is unpredictable, the transition from one branch to another can occur spontaneously, which is reflected in the presence in the source network of inclined edges that have their own direction and their own weights. The introduction of the method of transition from one branch of the oriented network to another at the time of termination of its implementation due to the unpredictable influence of environmental factors ensures the distribution of risks between the components. The use of combinatorics of the proposed options for interactions in the state space, their implementation at different moments of iterations, their application with the synchronization of flow throughput can reduce the risks arising from the functioning of systems.

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Das, Sandip, Mathew Francis, Pavol Hell, and Jing Huang. "Recognition and Characterization of Chronological Interval Digraphs." Electronic Journal of Combinatorics 20, no. 3 (July 26, 2013). http://dx.doi.org/10.37236/2497.

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Interval graphs admit elegant structural characterizations and linear time recognition algorithms; on the other hand, the usual interval digraphs lack a forbidden structure characterization as well as a low-degree polynomial time recognition algorithm. In this paper we identify another natural digraph analogue of interval graphs that we call ”chronological interval digraphs”. By contrast, the new class admits both a forbidden structure characterization and a linear time recognition algorithm. Chronological interval digraphs arise by interpreting the standard definition of an interval graph with a natural orientation of its edges. Specifically, $G$ is a chronological interval digraph if there exists a family of closed intervals $I_v$, $v \in V(G)$, such that $uv$ is an arc of $G$ if and only if $I_u$ intersects $I_v$ and the left endpoint of $I_u$ is not greater than the left endpoint of $I_v$. (Equivalently, if and only if $I_u$ contains the left endpoint of $I_v$.)We characterize chronological interval digraphs in terms of vertex orderings, in terms of forbidden substructures, and in terms of a novel structure of so-called $Q$-paths. The first two characterizations exhibit strong similarity with the corresponding characterizations of interval graphs. The last characterization leads to a linear time recognition algorithm.

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Seifter, Norbert, and Vladimir I. Trofimov. "Reachability Relations and the Structure of Transitive Digraphs." Electronic Journal of Combinatorics 16, no. 1 (February 27, 2009). http://dx.doi.org/10.37236/115.

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In this paper we investigate reachability relations on the vertices of digraphs. If $W$ is a walk in a digraph $D$, then the height of $W$ is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed opposite to their orientation. Two vertices $u,v\in V(D)$ are $R_{a,b}$-related if there exists a walk of height $0$ between $u$ and $v$ such that the height of every subwalk of $W$, starting at $u$, is contained in the interval $[a,b]$, where $a$ ia a non-positive integer or $a=-\infty$ and $b$ is a non-negative integer or $b=\infty$. Of course the relations $R_{a,b}$ are equivalence relations on $V(D)$. Factorising digraphs by $R_{a,\infty}$ and $R_{-\infty,b}$, respectively, we can only obtain a few different digraphs. Depending upon these factor graphs with respect to $R_{-\infty,b}$ and $R_{a,\infty}$ it is possible to define five different "basic relation-properties" for $R_{-\infty,b}$ and $R_{a,\infty}$, respectively. Besides proving general properties of the relations $R_{a,b}$, we investigate the question which of the "basic relation-properties" with respect to $R_{-\infty,b}$ and $R_{a,\infty}$ can occur simultaneously in locally finite connected transitive digraphs. Furthermore we investigate these properties for some particular subclasses of locally finite connected transitive digraphs such as Cayley digraphs, digraphs with one, with two or with infinitely many ends, digraphs containing or not containing certain directed subtrees, and highly arc transitive digraphs.

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Austhof, Bethany, Patrick Bennett, and Nick Christo. "The Set of Ratios of Derangements to Permutations in Digraphs is Dense in $[0,1/2]$." Electronic Journal of Combinatorics 29, no. 1 (January 28, 2022). http://dx.doi.org/10.37236/10293.

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A permutation in a digraph $G=(V, E)$ is a bijection $f:V \rightarrow V$ such that for all $v \in V$ we either have that $f$ fixes $v$ or $(v, f(v)) \in E$. A derangement in $G$ is a permutation that does not fix any vertex. Bucic, Devlin, Hendon, Horne and Lund proved that in any digraph, the ratio of derangements to permutations is at most $1/2$. Answering a question posed by Bucic, Devlin, Hendon, Horne and Lund, we show that the set of possible ratios of derangements to permutations in digraphs is dense in the interval $[0, 1/2]$.

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Francis, Mathew C., Pavol Hell, and Dalu Jacob. "On the Kernel and Related Problems in Interval Digraphs." Algorithmica, July 19, 2022. http://dx.doi.org/10.1007/s00453-022-01010-1.

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Meyerowitz, Aaron. "Tiling the Line with Triples." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AA,..., Proceedings (January 1, 2001). http://dx.doi.org/10.46298/dmtcs.2282.

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International audience It is known the one dimensional prototile $0,a,a+b$ and its reflection $0,b,a+b$ always tile some interval. The subject has not received a great deal of further attention, although many interesting questions exist. All the information about tilings can be encoded in a finite digraph $D_{ab}$. We present several results about cycles and other structures in this graph. A number of conjectures and open problems are given.In [Go] an elegant proof by contradiction shows that a greedy algorithm will produce an interval tiling. We show that the process of converting to a direct proof leads to much stronger results.

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Journal articles on the topic 'Interval digraphs'

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