1. Heterogeneous aspirations promote cooperation in the prisoner's dilemma gameMatjaž Perc, Zhen Wang, 2010, original scientific article Abstract: To be the fittest is central to proliferation in evolutionary games. Individuals thus adopt the strategies of better performing players in the hopeof successful reproduction. In structured populations the array of those that are eligible to act as strategy sources is bounded to the immediate neighbors of each individual. But which one of these strategy sources should potentially be copied? Previous research dealt with this question either by selecting the fittest or by selecting one player uniformly at random. Here we introduce a parameter that interpolates between these two extreme options. Setting equal to zero returns the random selection of the opponent, while positive favor the fitter players. In addition, we divide the population intotwo groups. Players from group select their opponents as dictated by the parameter , while players from group do so randomly irrespective of . We denote the fraction of players contained in groups and by and , respectively. The two parameters and allow us to analyze in detail how aspirations in the context of the prisoner's dilemma game influence the evolution of cooperation. We find that for sufficiently positive values of there exist a robust intermediate for which cooperation thrives best. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction networks. We also provide complete phase diagrams depicting the dependence of the impact of and for different values of , and contrast the validity of ourconclusions by means of an alternative model where individual aspiration levels are subject to evolution as well. Our study indicates that heterogeneity in aspirations may be key for the sustainability of cooperation in structured populations. Keywords: evolutionary game theory, prisoner's dilemma, spatial games, aspirations, social systems, physics and society Published: 19.06.2017; Views: 625; Downloads: 239 Full text (822,95 KB) This document has many files! More...

2. Optimization methods for solving transportation problems on networksKatja Prnaver, 2011, dissertation Abstract: In this thesis we study problems from real situations, which can be applied to network
graphs and solved using mathematical graph theory.
We start with the problem of oriented network design. The problem originates from
networks, where the flow over the arcs is important and many times limited with the capacity
of the networks. There are several techniques and results on the problem of assigning the
flow through the network channels. In our problem, we try to find the optimal network
structure, which could be used in the design phase of the network. With metaheuristics,
we search for optimal network structures for a given number of nodes. We define triangle
neighborhood and compare the results of the algorithm with the conjecture by Choplin et
al. [8].
Further, we study the problem of order picking and order batching in block structured
warehouses. For order picking problem, we present the extension of a dynamic programming
algorithm by Ratliff and Rosenthal [42], which enables the development of an algorithm for
an unlimited number of blocks. In order to achieve this, a new presentation of states and
transitions of dynamic programming algorithm is given. We prove that the resulting path is
optimal for the given structure. We compare the optimal path lengths to the results found in
literature and also investigate the impact of warehouse layout parameters onto the routing.
Closely related to the problem of order picking, we investigate the order batching problem.
We discuss the variation of the order batching problem with time windows and present
the algorithmic approach to solving the problem. The previously presented optimal path
algorithm is applied in the algorithm to ensure even better quality of results. We introduce
the evaluation function of a batch and compare the results of the algorithm with the test
data from the literature as well as with data from the real warehouse.
We conclude by summarizing the results and stating some possible extensions and further
work. Keywords: graph theory, networks, optimization, shortest path problem, traveling salesman problem, algorithms, metaheuristics, order batching Published: 03.06.2011; Views: 4074; Downloads: 184 Full text (925,86 KB) 
3. Chepoi Victor, Dragan Feodor F., Vaxes Yann: Distance and routing labeling schemes for nonpositively curved plane graphs. J. Algorithms 61 (2006), no. 2, 6088.Boštjan Brešar, 2006, review, book review, critique Keywords: mathematics, graph theory, distance labeling scheme, routing labeling scheme, efficient algorithms Published: 31.05.2012; Views: 1130; Downloads: 18 Link to full text 
4. Uncertainties facilitate aggressive behavior in a spatial hawkdove gameMatjaž Perc, 2007, original scientific article Abstract: We study effects of additive spatiotemporal random variations, introduced to the payoffs of a spatial hawkdove game, on the evolution of the reconciliatory and the aggressive strategy. We show that uncertainties facilitate aggressive behavior for a broad range of resource values. In particular, aggressors thrive best if stochastic influences are of the order of magnitude of deterministic payoff values. We argue that random payoff variations are potent and plausible promoters of aggressive behavior in human as well as animal societies if only the hawkdove game payoff ranking applies. Keywords: evolutionary game theory, hawkdove game, noise, spatial games Published: 31.05.2012; Views: 1120; Downloads: 35 Link to full text 
5. Fuzzy Logic Model for the performance benchmarking of sugar plants by considering best available techniquesDamjan Krajnc, Miro Mele, Peter Glavič, 2007, original scientific article Abstract: This paper deals with the problem of performance benchmarking of traditional beet sugar plants, by considering Best Available Techniques (BAT) for beet sugar production, as determined by the Integrated Pollution Prevention and Control (IPPC) Directive. A Fuzzy Logic Model, based on fuzzy set theory, was constructed for this purpose, in order to compare the performances of sugar plants within the sector's best standards, as expressed in the Reference Document on BAT. The effectiveness of the model was tested in the case study,in which three sugar plants were benchmarked against the BAT regarding the consumption of energy, water, raw materials and the production of wastes, wastewater, byproducts and the main product. The model was recognized as helpful for the benchmarking needs of sugar plants. In addition, by integrating BAT Reference Document analysis into the model, it provides IPPC permitting authorities with an objective method and uniform BAT benchmarks to manage permitting process. Keywords: chemical processing, beet sugar production, sugar industry, clean technologies, performance benchmarking, IPPC Directive, technology performance assessment, fuzzy set theory, best available techniques, IPPC permitting process Published: 31.05.2012; Views: 1782; Downloads: 71 Link to full text 
6. Thermal vibrational analysis for simply supported beam and clamped beamJurij Avsec, Maks Oblak, 2007, original scientific article Abstract: The presented paper shows how the temperature field in beams has impact on vibrations of beams. Due to the relatively high possible temperature variations in beams we have developed the mathematical model where fundamental thermomechanical properties of state are functions of temperature such as modulus of elasticity, Poisson number, linear expansion coefficient, shear modulus and some other important thermodynamic properties of state. The detailed analysis shows, that also small changes of temperature cause significant changes of natural frequencies for beams. The comparison between our analytical model and experimental data shows good agreement. In the presented paper it is possible to find for the first time in scientific literature the application of the combination of statistical thermodynamics and the theory of vibration at the same time. Keywords: statistical thermomechanics, vibrations, vibrational theory, temperature effects, simply supported beams, clamped beams, thermomechanical properties Published: 31.05.2012; Views: 978; Downloads: 67 Link to full text 
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9. On edge connectivity of direct products of graphsXiangLan Cao, Špela Brglez, Simon Špacapan, Elkin Vumar, 2011, original scientific article Abstract: Let ▫$lambda(G)$▫ be the edge connectivity of ▫$G$▫. The direct product of graphs ▫$G$▫ and ▫$H$▫ is the graph with vertex set ▫$V(G times H) = V(G) times V(H)$▫, where two vertices ▫$(u_1,v_1)$▫ and ▫$(u_2,v_2)$▫ are adjacent in ▫$G times H$▫ if ▫$u_1u_2 in E(G)$▫ and ▫$v_1v_2 in E(H)$▫. We prove that ▫$lambda(G times K_n) = min{n(n1)lambda(G), (n1)delta(G)}$▫ for every nontrivial graph ▫$G$▫ and ▫$n geqslant 3$▫. We also prove that for almost every pair of graphs ▫$G$▫ and ▫$H$▫ with ▫$n$▫ vertices and edge probability ▫$p$▫, ▫$G times H$▫ is ▫$k$▫connected, where ▫$k=O((n/log n)^2)$▫. Keywords: mathematics, graph theory, combinatorial problems, connectivity, direct product, graph product, separating set Published: 01.06.2012; Views: 1634; Downloads: 192 Link to full text 
10. 2local 3/4competitive algorithm for multicoloring hexagonal graphsPetra Šparl, Janez Žerovnik, 2005, original scientific article Abstract: An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference.A cellular network is generally modeled as a subgraph of the infinite triangular lattice. Frequency assignment problem can be abstracted asa multicoloring problem on a weighted hexagonal graph, where the weights represent the number of calls to be assigned at vertices. In this paper we present a distributed algorithm for multicoloring hexagonal graphs using only the local clique numbers ▫$omega_1(v)$▫ and ▫$omega_2(v)$▫ at each vertex v of the given hexagonal graph, which can be computed from local information available at thevertex. We prove the algorithm uses no more than ▫$4omega(G)/3$▫ colors for any hexagonal graph G, without explicitly computing the global clique number ▫$omega(G)$▫. We also prove that our algorithm is 2local, i.e., the computation at a vertex v ▫$in$▫ G uses only information about the demands of vertices whose graph distance from v is less than or equal to 2. Keywords: mathematics, graph theory, graph colouring, 2local distributed algorithm, cellular networks, frequency planning Published: 01.06.2012; Views: 1453; Downloads: 73 Link to full text 