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We consider the Hegselmann-Krause model for opinion dynamics and study the evolution of the system under various settings. We first analyze the termination time of the synchronous Hegselmann-Krause dynamics in arbitrary finite dimensions and show that the termination time in general only depends on the number of agents involved in the dynamics. To the best of our knowledge, that is the sharpest bound...
We study a linear multihop network that is formed by wireless devices that can directly communicate pairwise whenever two devices are within range of each other. This Device-to-Device communication model is expected to play a significant role in future 5G wireless networks due to its advantages (e.g., cellular offloading, increased throughput and low cost/energy communication). In such networks, devices...
Intercell interference has been known as a crucial issue in heterogeneous networks where different transmitter-receiver pairs compete for system resources. We solve this problem in two steps. We firstly assign the macrocell user with the optimum number of subchannels, which just guarantee the required quality of service. Then, the remaining subchannels are left to be shared by a large number of small...
Tonal music has had a rich history in Video Games and movies, and in fact, music generation has played a minor role in the history of game music as well. Recent developments in Music Theory has derived representions of chord progressions using geometric topologies. Unlike prior generative music, the framework proposed in this paper attempts to approach tonal music generation by building networks of...
In their seminal paper [1], Orda, Rom and Shimkin have already studied fully symmetric routing games, i.e. games in which all players have the same sources, destinations, demands and costs. They established the uniqueness of an equilibrium in these games. We extend their result to weaker forms of symmetry, which does not require a common source or destination. Considering routing games, we provide...
Continuous selection theorem plays a key role in nonlinear problems arising in mathematics and applied science. Michael (1956) firstly established a famous continuous selection theorem. Browder (1968) proved a continuous selection theorem under the framework of para compact topological vector spaces. Since then, many authors have established continuous selection theorems under various assumptions...
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