The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

We consider the triangle-free process: given an integer n, start by taking a uniformly random ordering of the edges of the complete n-vertex graph Kn. Then, traverse the ordered edges and add each traversed edge to an (initially empty) evolving graph unless its addition creates a triangle. We study the evolving graph at around the time where n edges have been traversed for any fixed ε ∈ (0, 10)...

The direct costs of managing adverse outcomes from Australian health care are estimated to be $2 billion. The audit cycle is considered an important tool to assist in the preventive management of adverse outcomes.Australian guidelines for audit cycle design allow for comparison of data sets derived from similar surgical specialities. However a lack of data set standardisation inhibits meaningfu...

We introduce two techniques for proving termination of graph transformation systems. We do not fix a single initial graph, but consider arbitrary initial graphs (uniform termination), but also certain sets of initial graphs (non-uniform termination). The first technique, which can also be used to show non-uniform termination, uses a weighted type graph to assign weights to graphs. The second te...

We present a simple semi-supervised relation extraction system with large-scale word clustering. We focus on systematically exploring the effectiveness of different cluster-based features. We also propose several statistical methods for selecting clusters at an appropriate level of granularity. When training on different sizes of data, our semi-supervised approach consistently outperformed a st...

We develop a statistical mechanics based approach for studying semi–supervised clustering in graphs in the presence of must and cannot links. We focus on bi– cluster graphs, and study the impact of the semi–supervision by varying the constraint density and overlap between the clusters. Recent results for unsupervised clustering in sparse graphs indicate that there is a critical ratio of within–...

One of most commonly used methods of data mining is clustering. Its goal is to identify unknown yet interesting and useful patters in datasets. Clustering is considered as unsupervised, however recent years have shown a tendency toward incorporation external knowledge into clustering methods making them semi-supervised methods. Generally, all known types of clustering methods such as partitioni...

We consider directed graphs with edge labels from a semiring. We present an algorithm that allows efficient execution of queries for existence and weights of paths, and allows updates of the graph: adding nodes and edges, and changing weights of existing edges. We apply this method in the construction of matchbound certificates for automatically proving termination of string rewriting. We re-im...

In the task of community detection, there often exists some useful prior information. In this paper, a Semi-supervised clustering approach using a new Evidential Label Propagation strategy (SELP) is proposed to incorporate the domain knowledge into the community detection model. The main advantage of SELP is that it can take limited supervised knowledge to guide the detection process. The prior...

Analysis of opinions, known as opinion mining or sentiment analysis, has attracted a great deal of attention recently due to many practical applications and challenging research problems. In this article, we study two important problems, namely, opinion lexicon expansion and opinion target extraction. Opinion targets (targets, for short) are entities and their attributes on which opinions have ...