Application of ordinal correspondence analysis for submerged aquatic vegetation monitoring

The European Water Framework states that macrophyte communities (seaweeds and seagrass) are key indicators of the ecological health of lagoons. Furthermore, the restoration of these communities, especially the Zostera meadows, is one of the main objectives of the Berre lagoon restoration plan. Consequently, a monitoring programme of the main macrophyte species still present in the lagoon was initiated in 1996. This monitoring resulted in a sequence of 11 spatially structured annual tables consisting of the observed density of these species. These tables are processed in this study. First, we specify the principles of Beh's ordinal correspondence analysis (OCA), designed for ordered row/column categories, and compare this method to classical correspondence analysis (CA). Then, we show that OCA is straightforwardly adaptable for processing a sequence of ordered contingency tables like ours. Both OCA and CA are afterwards used to reveal and test the main patterns of spatio-temporal changes of two macrophyte species in the Berre lagoon: Ulva and Zostera. The results we obtained are compared and discussed.     

The Distribution of Sums of Certain I.I.D. Pareto Variates

ABSTRACT

Though the Pareto distribution is important to actuaries and economists, an exact expression for the distribution of the sum of n i.i.d. Pareto variates has been difficult to obtain in general. This article considers Pareto random variables with common probability density function (pdf) f(x) = (α/β) (1 + x/β)^α+1 for x > 0, where α = 1,2,… and β > 0 is a scale parameter. To date, explicit expressions are known only for a few special cases: (i) α = 1 and n = 1,2,3; (ii) 0 < α < 1 and n = 1,2,…; and (iii) 1 < α < 2 and n = 1,2,…. New expressions are provided for the more general case where β > 0, and α and n are positive integers. Laplace transforms and generalized exponential integrals are used to derive these expressions, which involve integrals of real valued functions on the positive real line. An important attribute of these expressions is that the integrands involved are non oscillating.     

Imaging convex quadrilateral inclusions in uniform conductors from electrical boundary measurements

We demonstrate simulation-based Bayesian imaging from electrical impedance tomographic data, by summarizing the set of conductance images which could give rise to the data. The forward map from conductance image to data requires the solution of a partial differential equation subject to boundary conditions. We develop the example of recovering an unknown convex polygonal insulating inclusion within an object made of otherwise uniformly conducting material, and illustrate our methods with noisy synthetic data. Sampling is carried out using Markov chain Monte Carlo with the efficiency of the algorithm investigated over a range of noise levels.     

A HEURISTIC PROCEDURE FOR DETERMINING IN-PROCESS INVENTORIES

Most prior studies that examine in-process inventory requirements associated with a manufacturing facility employ an optimizing algorithm; this article proposes a heuristic procedure for determining such requirements. A procedure is given for determining “active” and “banked” work-in-process requirements. The two are combined to give total in-process requirements. A key factor presented in the paper is the relationship between in-process inventory requirements and the “balancing” of a production facility. Most prior researchers examine these problems independently. It will be shown that both problems can be resolved concurrently. The concepts are applicable to both an existing as well as a new manufacturing facility.