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Linear recognition of generalized Fibonacci cubes $Q_h (111)$
Yoomi Rho, Aleksander Vesel, 2016, izvirni znanstveni članek

Opis: The generalized Fibonacci cube $Q_h(f)$ is the graph obtained from the $h$-cube $Q_h$ by removing all vertices that contain a given binary string $f$ as a substring. In particular, the vertex set of the 3rd order generalized Fibonacci cube $Q_h(111)$ is the set of all binary strings $b_1b_2 ... b_h$ containing no three consecutive 1’s. We present a new characterization of the 3rd order generalized Fibonacci cubes based on their recursive structure. The characterization is the basis for an algorithm which recognizes these graphs in linear time.
Ključne besede: graph theory, Fibonacci cubes, recognition algorithm
Objavljeno: 10.07.2017; Ogledov: 38; Prenosov: 0
.pdf Polno besedilo (803,81 KB)

Guarded subgraphs and the domination game
Gašper Košmrlj, Douglas F. Rall, Sandi Klavžar, Boštjan Brešar, 2015, izvirni znanstveni članek

Opis: V članku vpeljemo koncept zaščitenega podgrafa. Množica le-teh po definicji leži med množico konveksnih in 2-izometričnih podgrafov, hkrati pa ni primerljiva z množico izometričnimih podgrafov. Dokažemo nekatere metrične lastnosti zaščitenih podgrafov ter koncept uporabimo v dominacijski igri, v kateri dva igralca, Dominator in Zavlačevalka, izmenično izbirata vozlišča grafa, tako da vsako izbrano vozlišče poveča množico dominiranih vozlišč. Dominatorjev cilj je končati igro, tj. dominirati celoten graf, čim hitreje, medtem ko je Zavlačevalkin cilj odigrati čim več potez. Igralno dominacijsko število je število potez v igri, ko Dominator začne in oba igralca igrata optimalno. Kot glavni rezultat članka dokažemo, da igralno dominacijsko število grafa ni nikoli manjše, kot igralno dominacijsko število njegovega zaščitenega podgrafa. Predstavljenih je tudi več aplikacij tega rezultata.
Ključne besede: dominacijska igra, igralno dominacijsko številko, konveksni podgraf, (2-)izometrični podgraf
Objavljeno: 10.07.2017; Ogledov: 37; Prenosov: 0
.pdf Polno besedilo (690,85 KB)

Covering codes in Sierpiński graphs
Michel Mollard, Laurent Beaudou, Sandi Klavžar, Sylvain Gravier, Matjaž Kovše, 2010, izvirni znanstveni članek

Opis: Za dani graf ▫$G$▫ in celi števili ▫$a$▫ in ▫$b$▫ je ▫$(a,b)$▫-koda grafa ▫$G$▫ množica vozlišč ▫$C$▫, tako da ima vsako vozlišče iz ▫$C$▫ natanko ▫$a$▫ sosedov v ▫$C$▫, vsako drugo vozlišče pa natanko ▫$b$▫ sosedov v ▫$C$▫. V tem prispevku klasificiramo števila ▫$a$▫ in ▫$b$▫, za katera obstajajo ▫$(a,b)$▫-kode v grafih Sierpińskega.
Ključne besede: graph theory, codes in graphs, perfect codes, Sierpiński graphs
Objavljeno: 10.07.2017; Ogledov: 36; Prenosov: 0
.pdf Polno besedilo (786,68 KB)

Connectivity of Fibonacci cubes, Lucas cubes, and generalized cubes
Jernej Azarija, Sandi Klavžar, Jaehun Lee, Yoomi Rho, 2015, izvirni znanstveni članek

Opis: If ▫$f$▫ is a binary word and ▫$d$▫ a positive integer, then the generalized Fibonacci cube ▫$Q_d(f)$▫ is the graph obtained from the ▫$d$▫-cube ▫$Q_d$▫ by removing all the vertices that contain ▫$f$▫ as a factor, while the generalized Lucas cube ▫$Q_d(\stackrel{\leftharpoondown}{f})$▫ is the graph obtained from ▫$Q_d$▫ by removing all the vertices that have a circulation containing ▫$f$▫ as a factor. The Fibonacci cube ▫$\Gamma_d$▫ and the Lucas cube ▫$\Lambda_d$▫ are the graphs ▫$Q_d({11})$▫ and ▫$Q_d(\stackrel{\leftharpoondown}{11})$▫, respectively. It is proved that the connectivity and the edge-connectivity of ▫$\Gamma_d$▫ as well as of ▫$\Lambda_d$▫ are equal to ▫$\left\lfloor \frac{d+2}{3}\right\rfloor$▫. Connected generalized Lucas cubes are characterized and generalized Fibonacci cubes are proved to be 2-connected. It is asked whether the connectivity equals minimum degree also for all generalized Fibonacci/Lucas cubes. It was checked by computer that the answer is positive for all ▫$f$▫ and all ▫$d \le9$▫.
Ključne besede: Fibonacci cube, Lucas cube, generalized Fibonacci cube, generalized Lucas cube, connectivity, combinatorics on words
Objavljeno: 10.07.2017; Ogledov: 40; Prenosov: 0
.pdf Polno besedilo (740,04 KB)

A new characterization and a recognition algorithm of Lucas cubes
Andrej Taranenko, 2013, izvirni znanstveni članek

Opis: Fibonacci and Lucas cubes are induced subgraphs of hypercubes obtained by excluding certain binary strings from the vertex set. They appear as models for interconnection networks, as well as in chemistry. We derive a characterization of Lucas cubes that is based on a peripheral expansion of a unique convex subgraph of an appropriate Fibonacci cube.This serves as the foundation for a recognition algorithm of Lucas cubes that runs in linear time.
Ključne besede: graph theory, Lucas cubes, characterization, recognition algorithm
Objavljeno: 10.07.2017; Ogledov: 40; Prenosov: 0
.pdf Polno besedilo (563,10 KB)

Biology students' teacher opinions about the integration of ICT into the learning and teaching process
Andreja Špernjak, 2014, izvirni znanstveni članek

Opis: Biology laboratory work can be performed in various ways, even using information and communication technologies (ICT). Whether a teacher incorporates it into laboratory work is related to different factors, but educators can influence students’ beliefs about the value of ICT through their pedagogical practice. In our study, student teachers of biology gave opinions on how successfully university professors use ICT in the classroom, where they acquired most knowledge about ICT and their attitude towards using of ICT in laboratory work. Student teachers were critical about the knowledge and usage of ICT of university professors in class. During their student teachers mostly failed to acquire knowledge about ICT and practice in incorporating it into daily routines. These results will be presented to our university professors, at which time we will suggest how they could use ICT more effectively in daily practice because, on the one hand, they are responsible for students teacher attitudes and for the level of student teacher knowledge, while, on the others, they precipitate indirectly in forming the pupils’ attitudes and determining the level of the pupils’ knowledge of ICT. The study was done on 85 student teachers of biology. Attitudes toward ICT are statistically significant by gender.
Ključne besede: education, information and communication technology, ICT, gender studies
Objavljeno: 06.07.2017; Ogledov: 38; Prenosov: 0
.pdf Polno besedilo (166,92 KB)

Vortices determine the dynamics of biodiversity in cyclical interactions with protection spillovers
Matjaž Perc, Attila Szolnoki, 2015, izvirni znanstveni članek

Opis: If rock beats scissors and scissors beat paper, one might assume that rock beats paper too. But this is not the case for intransitive relationships that make up the famous rock-paper-scissors game. However, the sole presence of paper might prevent rock from beating scissors, simply because paper beats rock. This is the blueprint for the rock-paper-scissors game with protection spillovers, which has recently been introduced as a new paradigm for biodiversity in well-mixed microbial populations. Here we study the game in structured populations, demonstrating that protection spillovers give rise to spatial patterns that are impossible to observe in the classical rock-paper-scissors game.Weshow that the spatiotemporal dynamics of the system is determined by the density of stable vortices, which may ultimately transform to frozen states, to propagating waves, or to target waves with reversed propagation direction, depending further on the degree and type of randomness in the interactions among the species. If vortices are rare, the fixation to waves and complex oscillatory solutions is likelier. Moreover, annealed randomness in interactions favors the emergence of target waves, while quenched randomness favors collective synchronization. Our results demonstrate that protection spillovers may fundamentally change the dynamics of cyclic dominance in structured populations, and they outline the possibility of programming pattern formation in microbial populations.
Ključne besede: cyclical interactions, pattern formation, vortices, phase transitions, selforganization, biodiversity
Objavljeno: 03.07.2017; Ogledov: 32; Prenosov: 2
.pdf Polno besedilo (1,32 MB)

Self-organization towards optimally interdependent networks by means of coevolution
Zhen Wang, Attila Szolnoki, Matjaž Perc, 2014, izvirni znanstveni članek

Opis: Coevolution between strategy and network structure is established as a means to arrive at the optimal conditions needed to resolve social dilemmas. Yet recent research has highlighted that the interdependence between networks may be just as important as the structure of an individual network. We therefore introduce the coevolution of strategy and network interdependence to see whether this can give rise to elevated levels of cooperation in the prisonerʼs dilemma game. We show that the interdependence between networks self-organizes so as to yield optimal conditions for the evolution of cooperation. Even under extremely adverse conditions, cooperators can prevail where on isolated networks they would perish. This is due to the spontaneous emergence of a two-class society, with only the upper class being allowed to control and take advantage of the interdependence. Spatial patterns reveal that cooperators, once arriving at the upper class, are much more competent than defectors in sustaining compact clusters of followers. Indeed, the asymmetric exploitation of interdependence confers to them a strong evolutionary advantage that may resolve even the toughest of social dilemmas.
Ključne besede: coevolution, cooperation, interdependent networks, evolutionary games, collective phenomena, self-organization, phase transitions, physics of social systems
Objavljeno: 03.07.2017; Ogledov: 36; Prenosov: 1
.pdf Polno besedilo (887,51 KB)

Self-organization of punishment in structured populations
Matjaž Perc, Attila Szolnoki, 2012, izvirni znanstveni članek

Opis: Cooperation is crucial for the remarkable evolutionary success of the human species. Not surprisingly, some individuals are willing to bear additional costs in order to punish defectors. Current models assume that, once set, the fine and cost of punishment do not change over time. Here we show that relaxing this assumption by allowing players to adapt their sanctioning efforts in dependence on the success of cooperation can explain both the spontaneous emergence of punishment and its ability to deter defectors and those unwilling to punish them with globally negligible investments. By means of phase diagrams and the analysis of emerging spatial patterns, we demonstrate that adaptive punishment promotes public cooperation through the invigoration of spatial reciprocity, the prevention of the emergence of cyclic dominance, or the provision of competitive advantages to those that sanction antisocial behavior. The results presented indicate that the process of self-organization significantly elevates the effectiveness of punishment, and they reveal new mechanisms by means of which this fascinating and widespread social behavior could have evolved.
Ključne besede: cooperation, public goods, punishment, phase transitions, physics of social systems
Objavljeno: 03.07.2017; Ogledov: 35; Prenosov: 1
.pdf Polno besedilo (1,22 MB)

Punish, but not too hard: how costly punishment spreads in the spatial public goods game
Dirk Helbing, Attila Szolnoki, Matjaž Perc, György Szabó, 2010, izvirni znanstveni članek

Opis: We study the evolution of cooperation in spatial public goods games where, besides the classical strategies of cooperation (C) and defection (D), we consider punishing cooperators (PC) or punishing defectors (PD) as an additional strategy. Using a minimalist modeling approach, our goal is to separately clarify and identify the consequences of the two punishing strategies. Since punishment is costly, punishing strategies lose the evolutionary competition in case of well-mixed interactions. When spatial interactions are taken into account, however, the outcome can be strikingly different, and cooperation may spread. The underlying mechanism depends on the character of the punishment strategy. In the case of cooperating punishers,increasing the fine results in a rising cooperation level. In contrast, in the presence of the PD strategy, the phase diagram exhibits a reentrant transition as the fine is increased. Accordingly, the level of cooperation shows a non-monotonous dependence on the fine. Remarkably, punishing strategies can spread in both cases, but based on largely different mechanisms, which depend on the cooperativeness (or not) of punishers.
Ključne besede: evolutionary game theory, public goods, spatial games, punishment, social systems, moral
Objavljeno: 03.07.2017; Ogledov: 29; Prenosov: 0
.pdf Polno besedilo (823,76 KB)

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