The first three sections give a quick overview of Martin boundary theory and state the main results. The succeeding sections will flesh out the details, and give proofs and examples. Virtually all of the results below are classical. The article Doob (1959) and the book by Kemeny, Snell, and Knapp (1976) are good sources for additional details. A recent survey article by Wolfgang Woess (1994) ha...

Epstein, R., Duberstein, P., Fenton, J., Fiscella, K., Hoerger, M., Tancredi, D., Xing, G., Gramling, R., Mohile, S., Butow, P., Walczak, A., Tattersall, M., et al (2017). Effect of a patientcentered communication intervention on oncologist-patient communication, quality of life, and health care utilization in advanced cancer: The VOICE randomized clinical trial. JAMA Oncology, 3(1), 92-100. <a...

The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Λ, is classically estimated using the capacity of Λ with respect to the Green kernel G(x, y). We show that replacing the Green kernel by the Martin kernel G(x, y)/G(0, y) yields improved estimates, which are exact up to a factor of 2. These estimates are applied to random walks on lattices, and also t...

Consden, R., Gordon, A. H. & Martin, A. J. P. (1944). Biochem. J. 38, 224. Consden, R., Gordon, A. H. & Martin, A. J. P. (1945). Biochem. J. 39, xlvi. Consden, R., Gordon, A. H. & Martin, A. J. P. (1946a). Biochem. J. 40, 33. Consden, R., Gordon, A. H. & Martin, A. J. P. (1946b). Biochem. J. 40, 580. Consden, R., Gordon, A. H., Martin, A. J. P. & Synge, R. L. M. (1947). Biochem. J. 41, 596. Mar...

This evolutionarily and functionally sharp distinction between organelles and endosymbionts — protein import, or not — was crisply articulated by CavalierSmith and Lee [9]. It has proven to be exquisitely robust. Unless the Paulinella endosymbiont can be shown to possess a protein import apparatus, it is just another member in a long list of known cases of endosymbionts: the proteobacterial end...

H. M. Scott, or Scotty to his friends, was born in 1901 in Lincoln, Nebraska. He received his B.S. degree in 1924 from Oregon State College, his M.S. in 1927 from Kansas State College, and his Ph.D. from the University of Illinois in 1938. He held faculty positions at North Dakota State College (1927–1928), Kansas State College (1928–1941), the University of Connecticut (1941–1947), and the Uni...

I have always enjoyed games, especially when incorporated into the classroom. can still remember game my fifth-grade teachers had us play to explore colonizing a new world. One of most impactful games I’ve played is SET®, which has become go-to for mathematics as means exploring geometry, combinatorics, probability, statistics, and vector spaces (Larson Quinn et al., 1999; Waddell Jr., 2017). f...