Links between the Calkin-Wilif tree and the Stern-Brocot tree are discussed answering the questions: What is the jth vertex in the nth level of the Calkin-Wilf tree? A simple mechanism is described for converting the jth vertex in the nth level of the Calkin-Wilf tree into the jth entry in the nth level of the Stern-Brocot tree. We also provide a simple method for evaluating terms in the hyperb...

We present explicit formulas for computation of the neighbors of several elements in Farey subsequences.

We prove some new combinatorial properties of the set PER of all words w having two periods p and q which are coprimes and such that w = p + q 2 [4,3]. We show that aPERb U {a, b} = St n Lynd, where St is the set of the finite factors of all infinite Sturmian words and Lynd is the set of the Lyndon words on the alphabet {a, b}. It is also shown that aPERb U {a, b} = CP, where CP is the set of C...

In this paper, we revisit the analyses of Antonie Stern (1925) and Hans Lewy (1977) devoted to the construction of spherical harmonics with two or three nodal domains. Our method yields sharp quantitative results and a better understanding of the occurrence of bifurcations in the families of nodal sets.This paper is a natural continuation of our critical reading of A. Stern’s results for Dirich...

In this paper, we introduce a new approach to computeraided microtonal improvisation by combining methods for (1) interactive scale navigation, (2) real-time manipulation of musical patterns and (3) dynamical timbre adaption in solidarity with the respective scales. On the basis of the theory of well-formed scales we offer a visualization of the underlying combinatorial ramifications in terms o...

Vr. H., a 20ear-old Negro housewife, was apparently norimnal at birth except for small supernumeraryl digits on eaich of her 4 extremities. As a child she was able to keel) up with other children until her early teens when she noted easy fatigabilitv on moderate exertion and inability to run because of dvspnea and marked dizziness. At 15 years of age she had pleurisy an(l shortness of l)reathi ...

Thank you, Elaine, for that wonderful introduction and for all the support from the beginning of my faculty career. It’s a tremendous honor to be recognized with the Curt Stern Award by the ASHG, and I’d like to express my gratitude to the Awards Committee for this recognition. An award is really invested with meaning by its past recipients, and I encourage you to take a look at the list of pas...

Receiving the Curt Stern Award makes me think of the year 1956, when Stern, an extraordinaryDrosophila geneticist with broad-ranging interests, becamepresident of the American Society of Human Genetics. It’s also the year I was born. During the first year of my life, Stern presided over the Society’s 10th annual meeting, in Ann Arbor. There, he delivered a presidential address entitled “On porc...