Set Systems Containing Many Maximal Chains

The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size maximise the number of $(n+1)$-element chains in the power set $\mathcal{P}(\{1,2,\dots,n\})$? We will show that for each fixed $\alpha>0$ there is a family of $\alpha 2^n$ sets containing $(\alpha+o(1))n!$ such chains, and that this is asymptotically best possible. For smaller set systems we are unable to answer the question. We conjecture that a `tower of cubes' construction is extremal. We finish by mentioning briefly a connection to an extremal problem on posets and a variant of our question for the grid graph.Comment: 5 page

We Need Men: the Union Draft in the Civil War

Review of: We Need Men: The Union Draft in the Civil War. Geary, James W

Higgs Assisted Q-balls from Pseudo-Nambu-Goldstone Bosons

Motivated by recent constructions of TeV-scale strongly-coupled dynamics, either associated with the Higgs sector itself as in pseudo-Nambu-Goldstone boson (pNGB) Higgs models or in theories of asymmetric dark matter, we show that stable solitonic Q- balls can be formed from light pion-like pNGB fields carrying a conserved global quantum number in the presence of the Higgs field. We focus on the case of thick-wall Q-balls, where solutions satisfying all constraints are shown to exist over a range of parameter values. In the limit that our approximations hold, the Q-balls are weakly bound and parametrically large, and the form of the interactions of the light physical Higgs with the Q-ball is determined by the breaking of scale symmetry.Comment: 24 pages, 6 figures, 1 tabl

Collection and Preservation of Food Crop Germplasm with Wide Genetic Diversity

Discussion by Russell T. Johnson of a project envisaging a number of committees devoted to the genetic diversity of particular crops, and to assessing the adequacy and requirements of existing germplasm collections, documenting the collections in a way accessible throughout the world to scientists working on those crops, and planning for the long term preservation of germplasm. Four such committees were already extant for Wheat, Barley and Rye, Maize, Sorghum and Millet, and Rice. Agenda item presented at TAC Second Meeting, October 1971

Montclair High School: A Multi-dimensional GIS Approach to Tactical Emergency Response

“This marks the fourth shooting incident at a U.S. school within a week -- the second at a college or university -- and serves as a stunning reminder that it is impossible to know when and where violence will occur.” (Knapp, 02/15/2008) This quote, referencing the 2008 shooting at Northern Illinois University, is a stark reminder that the school systems in the United States are soft targets for acts of violence. Although it is almost impossible to predict such tragic events, it is possible to prepare, react, and respond to these actions in a timely manner to reduce loss of life and property. Advances in technology, particularly in geographic information systems (GIS), have given first responders the ability to respond to these occurrences more rapidly and efficiently. The GIS application created in this project supports the needs of first responders to enhance preparation and response to emergencies, in this case at Montclair High School, Montclair, California. Utilizing a variety of geospatial tools and software applications, the system will provide emergency personnel with a unique application or system designed to support a more effective and efficient response