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Erik Carlson

Publications and source records attributed to Erik Carlson.

3 recordsLinked to original sources

Numerical Approximation Methods for Antenna Radiation Patterns for Motus Wildlife Tracking Systems

As plans for offshore wind energy development increase in the US, the developing methods to monitor migratory birds and bats offshore is an important area of research. To contribute to this research, current guidance recommends the deployment of Motus Wildlife Tracking stations by each developer for pre- and post- construction monitoring. To understand the characteristics of each of the stations, calibration techniques are recommended for each deployment. Despite this, previous attempts to calibrate these stations has failed to provide sufficient detail to allow for high-resolution tracking techniques. In this paper, we introduce an affordable and robust methodology to calibrate stations in the off-shore environment and develop processes to turn this raw calibration data into a numerical approximation of the antennas radiation pattern.

q-bio.QM

Large Monochromatic Components of Small Diameter

Gyárfás conjectured in 2011 that every $r$-edge-colored $K_n$ contains a monochromatic component of bounded ("perhaps three") diameter on at least $n/(r-1)$ vertices. Letzter proved this conjecture with diameter four. In this note we improve the result in the case of $r=3$: We show that in every $3$-edge-coloring of $K_n$ either there is a monochromatic component of diameter at most three on at least $n/2$ vertices or every color class is spanning and has diameter at most four.

math.CO

Graphs with Many Hamiltonian Paths

A graph is \emph{hamiltonian-connected} if every pair of vertices can be connected by a hamiltonian path, and it is \emph{hamiltonian} if it contains a hamiltonian cycle. We construct families of non-hamiltonian graphs for which the ratio of pairs of vertices connected by hamiltonian paths to all pairs of vertices approaches 1. We then consider minimal graphs that are hamiltonian-connected. It is known that any order-$n$ graph that is hamiltonian-connected must have $\geq 3n/2$ edges. We construct an infinite family of graphs realizing this minimum.

math.CO