On a Unimodality Conjecture in Matroid Theory

A certain unimodal conjecture in matroid theory states the number of rank-r matroids on a set of size n is unimodal in r and attains its maximum at r=\lfloor n/2 \rfloor . We show that this conjecture holds up to r=3 by constructing a map from a class of rank-2 matroids into the class of loopless rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless matroids and matroids

Emerging technologies for sustainable irrigation: Selected papers from the 2015 ASABE and IA irrigation symposium

Citation: Lamm, F. R., Stone, K. C., Dukes, M. D., Howell, T. A., Sr., Robbins, J. W. D., Jr., & Mecham, B. Q. (2016). Emerging technologies for sustainable irrigation: Selected papers from the 2015 ASABE and IA irrigation symposium. Transactions of the Asabe, 59(1), 155-161. doi:10.13031/trans.59.11706This article is an introduction to the "Emerging Technologies in Sustainable Irrigation: A Tribute to the Career of Terry Howell, Sr." Special Collection in this issue of Transactions of the ASABE and the next issue of Applied Engineering in Agriculture, consisting of 16 articles selected from 62 papers and presentations at the joint irrigation symposium of ASABE and the Irrigation Association (IA), which was held in November 2015 in Long Beach, California. The joint cooperation on irrigation symposia between ASABE and IA can be traced back to 1970, and this time period roughly coincides with the career of Dr. Howell. The cooperative symposia have offered an important venue for discussion of emerging technologies that can lead to sustainable irrigation. This most recent symposium is another point on the continuum. The articles in this Special Collection address three major topic areas: evapotranspiration measurement and determination, irrigation systems and their associated technologies, and irrigation scheduling and water management. While these 16 articles are not inclusive of all the important advances in irrigation since 1970, they illustrate that continued progress occurs by combining a recognition of the current status with the postulation of new ideas to advance our understanding of irrigation engineering and science. The global food and water challenges will require continued progress from our portion of the scientific community. This article serves to introduce and provide a brief summary of the Special Collection. © 2016 American Society of Agricultural and Biological Engineers

Random tree growth by vertex splitting

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalises the preferential attachment model and Ford's $\alpha$-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from one to infinity, depending on the parameters of the model.Comment: 47 page

Reconstruction of the spin state

System of 1/2 spin particles is observed repeatedly using Stern-Gerlach apparatuses with rotated orientations. Synthesis of such non-commuting observables is analyzed using maximum likelihood estimation as an example of quantum state reconstruction. Repeated incompatible observations represent a new generalized measurement. This idealized scheme will serve for analysis of future experiments in neutron and quantum optics.Comment: 4 pages, 1 figur

Measurement of the Alpha Asymmetry Parameter for the Omega- to Lambda K- Decay

We have measured the alpha parameter of the Omega- to Lambda K- decay using data collected with the HyperCP spectrometer during the 1997 fixed-target run at Fermilab. Analyzing a sample of 0.96 million Omega- to Lambda K^-, Lambda to p pi- decays, we obtain alpha_Omega*alpha_Lambda = [1.33+/-0.33(stat)+/-0.52(syst)] x 10^{-2}. With the accepted value of alpha_Lambda, alpha_Omega is found to be [2.07+/-0.51(stat)+/-0.81(syst)] x 10^{-2}.Comment: 5 pages, 4 figures, to be appeared as a Rapid Communication in Phys. Rev.

Evidence for the Decay Sigma+ -> p mu+ mu-

We report the first evidence for the decay Sigma+ -> p mu+ mu- from data taken by the HyperCP experiment(E871) at Fermilab. Based on three observed events, the branching ratio is B(Sigma+ -> p,mu+,mu-) = [8.6 +6.6,-5.4(stat) +/-5.5(syst)] x 10**-8. The narrow range of dimuon masses may indicate that the decay proceeds via a neutral intermediate state, Sigma+ -> p P0, P0 -> mu+ mu-, with a P0 mass of 214.3 +/- 0.5 MeV/c**2 and branching ratio B(Sigma+ -> p P0; P0 -> mu+ mu-) = [3.1 +2.4,-1.(stat) +/-1.5(syst)] x 10**-8.Comment: As published in PR