In earlier work, we showed using Kulback-Leibler (KL) divergence that tags form a power law distribution very quickly. Yet there is one major observed deviation from the ideal power law distribution for the top 25 tags, a large “bump” in increased frequency for the top 7-10 tags. We originally hypothesized that the “bump” in the data could be caused by a preferential attachment mechanism. Howev...

This paper focuses on the break-taking behaviour pattern of long-distance freight vehicles, providing a new perspective on the study of behaviour patterns and simultaneously providing a reference for transport management departments and related enterprises. Based on Global Positioning System (GPS) trajectory data, we select stopping points as break-taking sites of long-distance freight vehicles...

The view size estimation plays an important role in query optimization. It has been observed that many data follow a power law distribution. In this paper, we consider the balls in bins problem where we place balls into N bins when the bin selection probabilities follow a power law distribution. As a generalization to the coupon collector’s problem, we address the problem of determining the exp...

Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed the Luria-Delbrück or Lea-Coulson model, is often assumed but seldom realistic. In this article, we generalise this model to different ...

Modern technologies not only provide a variety of communication modes (e.g., texting, cell phone conversation, and online instant messaging), but also detailed electronic traces of these communications between individuals. These electronic traces indicate that the interactions occur in temporal bursts. Here, we study intercall duration of communications of the 100,000 most active cell phone use...

In this paper, we estimate probability { } Y X P < when X and Y are two independent random variables from Dagum distribution. We obtain maximum likelihood estimator and its asymptotic distribution. We also perform a simulation study.

One of the central parts in the study of combinatorial optimization is to classify the NP-hard optimization problems in terms of their approximability. In this thesis we study the Minimum Vertex Cover (Min-VC) problem and the Minimum Dominating Set (Min-DS) problem in the context of so called power law graphs. This family of graphs is motivated by recent findings on the degree distribution of e...

We show the fallacies of the Zipfian and power-law views in quantitative analyses of city-size distributions and of the notion that they are superior, simpler, and more universal than q-exponential or Pareto II distributions because of the single-parameter assumption. Both sets of models have two parameters, but the q-exponential captures a scaling coefficient that is fundamental to understandi...

This thesis studies the characteristics of cascading failures in a simulated linear swingequation model for simple power networks. The model transitions from displaying only small average failure size to undergoing large average failure size as the loading of the system is increased. For some parameter values, the transition region becomes critical, and it exhibits failures of all sizes whose d...

Degree distribution models are incredibly important tools for analyzing and understanding the structure and formation of social networks, and can help guide the design of efficient graph algorithms. In particular, the Power-law degree distribution has long been used to model the structure of online social networks, and is the basis for algorithms and heuristics in graph applications such as inf...