M.Sc. Mathematics and Statisticshttp://hdl.handle.net/10464/28832017-12-12T23:33:07Z2017-12-12T23:33:07ZDynamics in large scale networksClements, Johnhttp://hdl.handle.net/10464/92382017-10-10T14:14:34ZDynamics in large scale networks
Clements, John
In this thesis we study the properties of two large dynamic networks, the
competition network of advertisers on the Google and Bing search engines and
the dynamic network of friend relationships among avatars in the massively
multiplayer online game (MMOG) Planetside 2. We are particularly interested
in removal patterns in these networks. Our main finding is that in both of
these networks the nodes which are most commonly removed are minor near
isolated nodes. We also investigate the process of merging of two large
networks using data captured during the merger of servers of Planetside 2.
We found that the original network structures do not really merge but rather
they get gradually replaced by newcomers not associated with the original
structures. In the final part of the thesis we investigate the concept of motifs
in the Barabási-Albert random graph. We establish some bounds on the
number of motifs in this graph.
Community Detection in Multi-Layer NetworksPichugina, Oksanahttp://hdl.handle.net/10464/73242017-10-10T14:14:34ZCommunity Detection in Multi-Layer Networks
Pichugina, Oksana
In the scope of the current thesis we review and analyse networks that are formed by nodes with several attributes. We suppose that different layers of communities are embedded in such networks, besides each of the layers is connected with nodes' attributes. For example, examine one of a variety of online social networks: an user participates in a plurality of different groups/communities – schoolfellows, colleagues, clients, etc. We introduce a detection algorithm for the above-mentioned communities. Normally the result of the detection is the community supplemented just by the most dominant attribute, disregarding others. We propose an algorithm that bypasses dominant communities and detects communities which are formed by other nodes' attributes. We also review formation models of the attributed networks and present a Human Communication Network (HCN) model. We introduce a High School Texting Network (HSTN) and examine our methods for that network.
Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards ModelsHuang, Wan-yihttp://hdl.handle.net/10464/72302017-10-10T14:14:34ZOptimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models
Huang, Wan-yi
Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a
limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction.
My master thesis research focuses on designing accelerated life testing experiments for reliability estimation.
We consider multiple step-stress ALT plans with censoring. The optimal stress levels and times of changing
the stress levels are investigated. We discuss the optimal designs under three optimality criteria. They are
D-, A- and Q-optimal designs. We note that the classical designs are optimal only if the model assumed is
correct. Due to the nature of prediction made from ALT experimental data, attained under the stress levels
higher than the normal condition, extrapolation is encountered. In such case, the assumed model cannot be
tested. Therefore, for possible imprecision in the assumed PH model, the method of construction for robust
designs is also explored.
Backbone Colouring of GraphsGolestanian, Arnooshhttp://hdl.handle.net/10464/71582017-10-10T14:14:34ZBackbone Colouring of Graphs
Golestanian, Arnoosh
Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H).
It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles.
In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method.
In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.