Asymptotic enumeration of incidence matrices

We discuss the problem of counting {\em incidence matrices}, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with $n$ ones as $n\to\infty$. We also give refined results for the asymptotic number of $i\times j$ incidence matrices with $n$ ones.Comment: jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda

A graph partition problem

Given a graph $G$ on $n$ vertices, for which $m$ is it possible to partition the edge set of the $m$-fold complete graph $mK_n$ into copies of $G$? We show that there is an integer $m_0$, which we call the \emph{partition modulus of $G$}, such that the set $M(G)$ of values of $m$ for which such a partition exists consists of all but finitely many multiples of $m_0$. Trivial divisibility conditions derived from $G$ give an integer $m_1$ which divides $m_0$; we call the quotient $m_0/m_1$ the \emph{partition index of $G$}. It seems that most graphs $G$ have partition index equal to $1$, but we give two infinite families of graphs for which this is not true. We also compute $M(G)$ for various graphs, and outline some connections between our problem and the existence of designs of various types

Communicating research with the public : evaluation of an invasive earthworm education program

Ecologists are increasingly encouraged by funding agencies and professional societies to communicate their research with the public. However, most receive relatively little training in how to do this effectively. Furthermore, evaluation of whether such an investment by ecologists actually achieves conservation objectives is rare. We created an education program, involving print, television, radio, and internet media, to increase awareness about earthworm invasions and to discourage anglers from dumping earthworm bait. Using pre- and post-surveys, we evaluated our program’s success in reaching its target audience and in changing knowledge and behavior. Few participants (4.1%) recalled seeing the program material and knowledge of the fact that earthworms are non-native in Alberta remained low (15.8% before, 15.1% after). Further, after being told about the negative effects of earthworms in forests, 46.7% of the anglers surveyed stated they would not change their bait disposal behavior in the future, with many commenting that they did not believe earthworms could be harmful. These results highlight the importance of evaluating education programs, rather than assuming they are successful. Given many participants' doubts that earthworms have negative effects, both regulations and education may be needed to reduce earthworm introductions

The instability of stellar structures intermediate between white dwarfs and neutron stars

Instability of stellar structures intermediate between dwarfs and neutron star

Surface flux transport modeling for solar cycles 15--21: effects of cycle-dependent tilt angles of sunspot groups

We model the surface magnetic field and open flux of the Sun from 1913 to 1986 using a surface flux transport model, which includes the observed cycle-to-cycle variation of sunspot group tilts. The model reproduces the empirically derived time evolution of the solar open magnetic flux, and the reversal times of the polar fields. We find that both the polar field and the axial dipole moment resulting from this model around cycle minimum correlate with the strength of the following cycle.Comment: Accepted for publication by Ap

Penetration and spreading of transverse jets of hydrogen in a Mach 2.72 airstream

Schlieren photography of flow distribution for transverse hydrogen jets from flat plate into Mach 2.72 airstrea

A general class of spreading processes with non-Markovian dynamics

In this paper we propose a general class of models for spreading processes we call the $SI^*V^*$ model. Unlike many works that consider a fixed number of compartmental states, we allow an arbitrary number of states on arbitrary graphs with heterogeneous parameters for all nodes and edges. As a result, this generalizes an extremely large number of models studied in the literature including the MSEIV, MSEIR, MSEIS, SEIV, SEIR, SEIS, SIV, SIRS, SIR, and SIS models. Furthermore, we show how the $SI^*V^*$ model allows us to model non-Poisson spreading processes letting us capture much more complicated dynamics than existing works such as information spreading through social networks or the delayed incubation period of a disease like Ebola. This is in contrast to the overwhelming majority of works in the literature that only consider spreading processes that can be captured by a Markov process. After developing the stochastic model, we analyze its deterministic mean-field approximation and provide conditions for when the disease-free equilibrium is stable. Simulations illustrate our results