Fixing numbers for matroids

Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maximum orbit size (under the action of the matroid automorphism group). We prove the fixing numbers for the cycle matroid and bicircular matroid associated with 3-connected graphs are identical. Many of these results have interpretations through permutation groups, and we make this connection explicit.Comment: This is a major revision of a previous versio

Planned improvements to the Owens Valley frequency-agile interferometer

Three small antennas will be added to the OVRO interferometer to form a five-element solar-dedicated array. This would provide up to 7 or 10 baselines (compared to the present 1 or 3). This would be sufficient to apply microwave diagnostics to most active region and burst sources. By using frequency-synthesis it would also provide an imaging capability comparable to that of an approximately 100 baseline interferometer. Expansion of the array is discussed

Series-parallel posets and the Tutte polynomial

AbstractWe investigate the Tutte polynomial f(P; t, z) of a series-parallel partially ordered set P. We show that f(P) can be computed in polynomial-time when P is series-parallel and that series-parallel posets having isomorphic deletions and contractions are themselves isomorphic. A formula for f(P∗) in terms of f(P) is obtained and shows these two polynomials factor over Z[t, z] the same way. We examine several subclasses of the class of series-parallel posets, proving that f(P) ≠ f(Q) for non-isomorphic posets P and Q in the largest of these classes. We also give excluded subposet characterizations of the various subclasses

Impulsive phase solar flare X-ray polarimetry

The pioneering observational work in solar flare X-ray polarimetry was done in a series of satellite experiments by Tindo and his collaborators in the Soviet Union; initial results showed high levels of polarization in X-ray flares (up to 40%), although of rather low statistical significance, and these were generally interpreted as evidence for strong beaming of suprathermal electrons in the flare energy release process. However, the results of the polarimeter flown by the Columbia Astrophysics Laboratory as part of the STS-3 payload on the Space Shuttle by contrast showed very low levels of polarization. The largest value (observed during the impulsive phase of a single event) was 3.4% + or - 2.2%. At the same time but independent of the observational work, Leach and Petrosian (1983) showed that the high levels of polarization in the Tindo results were difficult to understand theoretically, since the electron beam is isotropized on an energy loss timescale. A subsequent comparison by Leach, Emslie, and Petrosian (1985) of the impulsive phase STS-3 result and the above theoretical treatment shows that the former is consistent with several current models and that a factor of approximately 3 improvement in sensitivity is needed to distinguish properly among the possibilities

HOPE Longitudinal Study: Year 2 Results

Abstract pending

Random subtrees of complete graphs

We study the asymptotic behavior of four statistics associated with subtrees of complete graphs: the uniform probability $p_n$ that a random subtree is a spanning tree of $K_n$, the weighted probability $q_n$ (where the probability a subtree is chosen is proportional to the number of edges in the subtree) that a random subtree spans and the two expectations associated with these two probabilities. We find $p_n$ and $q_n$ both approach $e^{-e^{-1}}\approx .692$, while both expectations approach the size of a spanning tree, i.e., a random subtree of $K_n$ has approximately $n-1$ edges