Graph theory based QoE-driven cooperation stimulation for content dissemination in device-To-device communication

With multimedia dominating the digital contents, Device-To-Device (D2D) communication has been proposed as a promising data offloading solution in the big data area. As the quality of experience (QoE) is a major determining factor in the success of new multimedia applications, we propose a QoEdriven cooperative content dissemination (QeCS) scheme in this work. Specifically, all users predict the QoE of the potential connections characterized by the mean opinion score (MOS), and send the results to the content provider (CP). Then CP formulates a weighted directed graph according to the network topology and MOS of each potential connection. In order to stimulate cooperation among the users, the content dissemination mechanism is designed through seeking 1-factor of the weighted directed graph with the maximum weight thus achieving maximum total user MOS. Additionally, a debt mechanism is adopted to combat the cheat attacks. Furthermore, we extend the proposed QeCS scheme by considering a constrained condition to the optimization problem for fairness improvement. Extensive simulation results demonstrate that the proposed QeCS scheme achieves both efficiency and fairness especially in large scale and density networks.

Syzygies of the polynomial invariants of the Riemann tensor

This thesis introduces a novel way of writing polynomial invariants as network graphs, and applies this diagrammatic notation scheme, in conjunction with graph theory, to derive algorithms for constructing relationships (syzygies) between different invariants. These algorithms give rise to a constructive solution of a longstanding classical problem in invariant theory.

Intersection and partition graphs

This thesis reviews previous work done on both general partition graphs and existential partition graphs, which are a generalised form of general partition graphs, and extends some of the results.

Unleashing the vermin : vectored route-length minimization

We have posed a simple but interesting graph theoretic problem and posited a heuristic solution procedure, which we have christened as Vectored Route-length Minimization (VeRMin). Basically, it constitutes a re-casting of the classical “shortest route” problem in a strictly Euclidean space. We have presented only a heuristic solution process hoping that a formal proof will eventually emerge as the problem receives wider exposure within mathematical circles.

Discovering semantics from visualizations of film takes

In this paper, we study the application of a scene structure visualizing technique called Double-Ring Take-Transition-Diagram (DR-TTD). This technique presents takes and their transitions during a film scene via nodes and edges of a 'graph' consisting of two rings as its backbone. We describe how certain filmic elements such as montage, centre/cutaway, dialogue, temporal flow, zone change, dramatic progression, shot association, scene introduction, scene resolution, master shot and editing orchestration can be identified from a scene through the signature arrangements of nodes and edges in the DR-TTD.

Power graphs : a survey

This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.

Robust nonlinear distributed controller design for active and reactive power sharing in islanded microgrids

This paper presents a robust nonlinear distributed controller design for islanded operation of microgrids in order to maintain active and reactive power balance. In this paper, microgrids are considered as inverter-dominated networks integrated with renewable energy sources (RESs) and battery energy storage systems (BESSs), where solar photovoltaic generators act as RESs and plug-in hybrid electric vehicles as BESSs to supply power into the grid. The proposed controller is designed by using partial feedback linearization and the robustness of this control scheme is ensured by considering structured uncertainties within the RESs and BESSs. An approach for modeling the uncertainties through the satisfaction of matching conditions is also provided in this paper. The proposed distributed control scheme requires information from local and neighboring generators to communicate with each other and the communication among RESs, BESSs, and control centers is developed by using the concept of the graph theory. Finally, the performance of the proposed robust controller is demonstrated on a test microgrid and simulation results indicate the superiority of the proposed scheme under different operating conditions as compared to a linear-quadratic-regulator-based controller.

A new model to imitate the foraging behavior of Physarum polycephalum on a nutrient-poor substrate

Researches on Physarum polycephalum show that methods inspired by the primitive unicellular organism can construct an efficient network and solve some complex problems in graph theory. Current models simulating the intelligent behavior of Physarum are mainly based on Hagen-Poiseuille Law and Kirchhoff Law, reaction-diffusion, Cellular Automaton and multi-agent approach. In this paper, based on an assumption that the plasmodium of Physarum forages for food along the gradient of chemo-attractants on a nutrient-poor substrate, a new model is proposed to imitate its intelligent foraging behavior. The key point of the model is that the growth of Physarum is determined by the simple particle concentration field relating the distance to food source and the shape of food source on a nutrient-poor substrate. To verify this model, numerical experiments are conducted according to Adamatzky[U+05F3]s experiment. Results in spanning tree construction by this model are almost the same as those of Physarum and Oregonator model. The proposed model can also imitate Physarum to avoid repellents. Furthermore, the Euclidean Spanning tree built by this model is similar to its corresponding Minimal Euclidean Spanning tree.

Optimal radio labellings of complete m-ary trees

A radio labelling of a connected graph G is a mapping f : V (G) → {0, 1, 2, ...} such that | f (u) - f (v) | ≥ diam (G) - d (u, v) + 1 for each pair of distinct vertices u, v ∈ V (G), where diam (G) is the diameter of G and d (u, v) the distance between u and v. The span of f is defined as max_u, _{v ∈ V (G)} | f (u) - f (v) |, and the radio number of G is the minimum span of a radio labelling of G. A complete m-ary tree (m ≥ 2) is a rooted tree such that each vertex of degree greater than one has exactly m children and all degree-one vertices are of equal distance (height) to the root. In this paper we determine the radio number of the complete m-ary tree for any m ≥ 2 with any height and construct explicitly an optimal radio labelling.