Approximate closed-form formulas for the zeros of the Bessel Polynomials

We find approximate expressions x(k,n) and y(k,n) for the real and imaginary parts of the kth zero z_k=x_k+i y_k of the Bessel polynomial y_n(x). To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros of the normalized Bessel polynomials. Thus, these zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then, a fit to the real and imaginary parts as functions of k and n is obtained. It is shown that the resulting complex number x(k,n)+i y(k,n) is O(1/n^2)-convergent to z_k for fixed kComment: 9 pages, 2 figure

Impact of the commercial fishery on the population of bait shrimp (Penaeus spp.) in Biscayne Bay, 1986

Monthly population size of bait shrimp in the Bay was estimated from December 1984 to July 1985. Growth rates for male and female P. duorarum showed that pink shrimp exhibit a mean residence time in the nursery area (Biscayne Bay) of approximately 21 weeks. Monthly mortality rates were determined for each sex of pink shrimp. It was estimated that 23% and 26% of the male and female monthly population size, respectively, was absorbed by both the fishery and ecosystem monthly. Monthly proportion of the standing stock expected to die exclusively through fishing was 6.5% and 6.0% for males and females respectively. Estimates of emigration rates showed that approximately 4.0% of the population was lost from the Bay system each month. This surplus production was about 50% of the average monthly catch by the fleet. Fishing mortality represents only 8 - 9% of the losses to the shrimp population. The biggest source of loss is emigration, suggesting that most shrimp beyond the size at recruitment (to the fishery) are not utilized for food while in the Bay. Thus, it appears that the direct impact of the fishery on the bait shrimp population is relatively small. (PDF contains 46 pages

Searching for Bayesian Network Structures in the Space of Restricted Acyclic Partially Directed Graphs

Although many algorithms have been designed to construct Bayesian network structures using different approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function and a search procedure (although some methods combine the two). Within the score+search paradigm, the dominant approach uses local search methods in the space of directed acyclic graphs (DAGs), where the usual choices for defining the elementary modifications (local changes) that can be applied are arc addition, arc deletion, and arc reversal. In this paper, we propose a new local search method that uses a different search space, and which takes account of the concept of equivalence between network structures: restricted acyclic partially directed graphs (RPDAGs). In this way, the number of different configurations of the search space is reduced, thus improving efficiency. Moreover, although the final result must necessarily be a local optimum given the nature of the search method, the topology of the new search space, which avoids making early decisions about the directions of the arcs, may help to find better local optima than those obtained by searching in the DAG space. Detailed results of the evaluation of the proposed search method on several test problems, including the well-known Alarm Monitoring System, are also presented

Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators

We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a trigonometric polynomial. These matrices can be used to find the exact spectrum of an elliptic operator in particular cases and in general, to give insight into the properties of the solution of the spectral problem. As examples, the analytical index and the eigenvalues of the Dirac operator on the torus and on the sphere are obtained and as an application of this technique, the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page

The Non-Abelian Self Dual String on the Light Cone

We construct the scalar profile for the non-abelian self dual string connecting two M5-branes compactified on a light-like circle. The construction is based on a conjectured modified version of Nahm's equations describing a D2-brane, with a magnetic field on it, suspended between two D4-branes. Turning on a constant magnetic field on the D2-brane corresponds to a boost in the eleventh direction. In the limit of infinite boost the D4-branes correspond to light-like compactified M5-branes. The solution for the scalar profile of the brane remains finite in this limit and displays all the correct expected features such as smooth interpolation between the unbroken and broken phase with the correct value for the Higgs field at infinity.Comment: 13 pages, LaTeX 2e, 2 figure

A novel evolutionary formulation of the maximum independent set problem

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The resulting heuristic has been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and has been found to be competitive when compared to several of the other heuristics that have also been tested on those graphs

Comparison of the physical properties of vermicompost from paper mill sludge and green compost as substitutes for peat-based potting media

The properties of vermicompost, green compost, and their mixes as substitutes for peat were evaluated regarding their recommendation for potting media. The mixes with a maximum of 50% of vermicompost or green compost had acceptable air filled porosity (AFP) and easily available water (EAW). In the vermicompost the level of organic matter (OM), dry bulk density (DBD) and shrinkage were acceptable; however, the AFP and EAW together were not at the recommended level in the different batches; as a consequence, vermicompost should not be used alone for potting media. In the green compost, the level of OM was low which increased the DBD and consequently the AFP was diminished. The particle size distribution (PSD) was different among peat, vermicompost and green compost. The coarse peat had the lower proportion of particles from 0.25 to 2.00 mm (41%) whereas the green compost had the lower coarseness index (CI: percentage by weight of particles larger than 0.5 mm in diameter), 48.4%. The direct effect of the PSD, OM and DBD in the water and air availability was confirmed. Moreover, there were high correlations between the OM, DBD, shrinkage, pore volume and PSD with the water release curve. Those properties should be considered in order to increase the level of substitution of vermicompost in peat-based potting media