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In this paper we study group-based Markov models of evolution and their mixtures. In the algebreo-geometric setting, group-based phylogenetic tree models correspond to toric varieties, while their mixtures correspond to secant and join varieties. Determining properties of these secant and join varieties can aid both in model selection and establishing parameter identifiability. Here we explore the first natural geometric property of these varieties: their dimension. The expected projective dimension of the join variety of a set of varieties is one more than the sum of their dimensions. A join variety that realizes the expected dimension is nondefective. Nondefectiveness is not only interesting from a geometric point-of-view, but has been used to establish combinatorial identifiability for several classes of phylogenetic mixture models. In this paper, we focus on group-based models where the equivalence classes of identified parameters are orbits of a subgroup of the automorphism group of the group defining the model. In particular, we show that, for these group-based models, the variety corresponding to the mixture of $r$ trees with $n$ leaves is nondefective when $n \geq 2r+5$. We also give improved bounds for claw trees and give computational evidence that 2-tree and 3-tree mixtures are nondefective for small~$n$., Comment: 24 pages, 4 figures

We introduce the package PhylogeneticTrees for Macaulay2 which allows users to compute phylogenetic invariants for group-based tree models. We provide some background information on phylogenetic algebraic geometry and show how the package PhylogeneticTrees can be used to calculate a generating set for a phylogenetic ideal as well as a lower bound for its dimension. Finally, we show how methods within the package can be used to compute a generating set for the join of any two ideals.

Presentation given at the Satellite Oceanography Users Workshop, Melbourne, Australia, 9 -11 Nov 2015.

Modelling of pavement performance deterioration is a critical engineering process in Pavement Management Systems. Most of the existing Airport Pavement Management Systems (APMS) employ limited surface distresses in their performance evaluation models. These systems may not serve the objectives of some agencies. It is essential for an effective APMS to include evaluation models that adequately address the specific needs of the agency. This paper presents the development of a unique pavement deterioration index, i.e., the Condition Rating Index, developed for 1 Canadian Air Division (1 CAD). This index is modelled to serve the specific needs of 1 CAD effectively. Performance prediction models for the various classes of pavements are developed based on Markov Chains. The prioritization methodology employed also reflects the needs of 1 CAD. Consequently, this paper investigates the quantification and prediction of Foreign Object Damage (FODp). The FODp Index is developed as well as defined. Prediction models for FODp are developed along with the establishment of critical states of the FODp Index.Key words: airport pavement management system, Condition Rating Index, pavement performance evaluation models, Foreign Object Damage, 1 Canadian Air Division.

With funding from the NOAA Fisheries Pacific Islands Regional Office, the Human Dimensions Research Program (HDRP) at the NOAA Fisheries Pacific Islands Fisheries Science Center conducted a survey of randomly selected residents of CNMI and Guam to provide information for a management plan for the Monument. Designation of the Monument was accompanied by social debate over the merits of designation, the potential economic benefits, increased federal management in the archipelago, the impacts to fishermen and fishing communities, and other effects (Kotowicz and Richmond, 2013). Now that the Monument has been established and management planning is ongoing, Monument managers believe there is a need for research to define CNMI and Guam residents' management preferences and their perceptions of Monument effects so this information is available to managers as they develop and begin to implement the plan.

It is common practice in most Canadian provinces to permit right turns on red at signalized intersections. At intersections with a high volume of pedestrian traffic, the opportunity to turn right on red may be critical to satisfy right turn demand. However, in order to properly time the traffic control signal display at a signalized intersection, the saturation flow rates for each lane or lane group of the intersection must be known. Six signalized intersections were studied in Kingston, Ontario, where saturation flow rates for right turns were measured as a function of conflicting through traffic. From these measurements, estimations of the gap size required for a right turn movement were made. A regression analysis resulted in the production of a simple equation for estimating right turn on red saturation flow rates. It was found that the gap acceptance behaviour of drivers varied both spatially and temporally. Key words: saturation flow rates, signalized intersections, capacity, gap acceptance.

The determination of the optimum phase scheme, cycle time, and green split for an isolated traffic signal is usually a very tedious and time-consuming activity. Several computer packages, such as the Micro-Sintral program, have been developed to assist in such situations by automating many of the calculations for a given set of inputs. Unfortunately, the inputs are often equally difficult to determine, and as they may depend upon the ultimate outcome of the optimization process, several time-consuming iterations, during which new input values must be calculated, are required. This paper presents a program called Signal Expert which automates the above iterations and therefore greatly reduces the traffic engineer's efforts in generating a new signal timing plan based on the rather sophisticated procedures that are outlined in the Canadian Capacity Guide. The benefits of applying this new program are illustrated and discussed using the example intersections that are analyzed in the Canadian Capacity Guide and in the Micro-Sintral User's Manual. Key words: isolated intersections, capacity, delay.