Axiomization of the center function on trees.

We give a new, short proof that four certain axiomatic properties uniquely define the center of a tree.

Generalized centrality in trees

In 1982, Slater defined path subgraph analogues to the center, median, and (branch or branchweight) centroid of a tree. We define three families of central substructures of trees, including three types of central subtrees of degree at most D that yield the center, median, and centroid for D = 0 and Slater's path analogues for D = 2. We generalize these results concerning paths and include proofs that each type of generalized center and generalized centroid is unique. We also present algorithms for finding one or all generalized central substructures of each type.

Systems approaches to animal disease surveillance and resource allocation: methodological frameworks for behavioral analysis

While demands for animal disease surveillance systems are growing, there has been little applied research that has examined the interactions between resource allocation, cost-effectiveness, and behavioral considerations of actors throughout the livestock supply chain in a surveillance system context. These interactions are important as feedbacks between surveillance decisions and disease evolution may be modulated by their contextual drivers, influencing the cost-effectiveness of a given surveillance system. This paper identifies a number of key behavioral aspects involved in animal health surveillance systems and reviews some novel methodologies for their analysis. A generic framework for analysis is discussed, with exemplar results provided to demonstrate the utility of such an approach in guiding better disease control and surveillance decisions

Axiomization of the center function on trees.

We give a new, short proof that four certain axiomatic properties uniquely define the center of a tree

Generalized centrality in trees

In 1982, Slater defined path subgraph analogues to the center, median, and (branch or branchweight) centroid of a tree. We define three families of central substructures of trees, including three types of central subtrees of degree at most D that yield the center, median, and centroid for D = 0 and Slater's path analogues for D = 2. We generalize these results concerning paths and include proofs that each type of generalized center and generalized centroid is unique. We also present algorithms for finding one or all generalized central substructures of each type

Fake News and Indifference to Truth

State of the Union Addresses (SOUA) by two recent US Presidents, President Obama (2016) and President Trump (2018), and a series of recent of tweets by President Trump, are analysed by means of the data mining technique, sentiment analysis. The intention is to explore the contents and sentiments of the messages contained, the degree to which they dier, and their potential implications for the national mood and state of the economy. President Trump's 2018 SOUA and his sample tweets are identied as being more positive in sentiment than President Obama's 2016 SOUA. This is conrmed by bootstrapped t tests and non-parametric sign tests on components of the respective sentiment scores. The issue of whether overly positive pronouncements amount to self-promotion, rather than intrinsic merit or sentiment, is a topic for future research

Bayesian estimation for selective trace gas detection

We present a Bayesian estimation analysis for a particular trace gas detection technique with species separation provided by differential diffusion. The proposed method collects a sample containing multiple gas species into a common volume, and then allows it to diffuse across a linear array of optical absorption detectors, using, for example, high-finesse Fabry-Perot cavities. The estimation procedure assumes that all gas parameters (e.g. diffusion constants, optical cross sections) are known except for the number population of each species, which are determined from the time-of-flight absorption profiles in each detector