Papers by Jason Rosenhouse
Bioscience, 2006
News media coverage of the controversy surrounding recent attempts to insert creationism into pub... more News media coverage of the controversy surrounding recent attempts to insert creationism into public school science curricula-this time in the form of "intelligent design"-has generated miles of copy and hours of television footage. The quality of that reporting varies widely, depending on the media outlet. Often, reporters with no scientific training are assigned to report on evolution-creationism controversies, which inevitably leads to distortions of the relevant science. A misconceived concern for balance frequently results in equal time being accorded to biologists and creationists, creating the illusion of scientific equivalence. At other times, a clear bias toward creationism is revealed, especially on cable television. Focusing mainly on recent treatments, this article analyzes and critiques specific stories, as well as trends and patterns in coverage in newspapers, magazines, and television; it concludes with suggestions of ways in which scientists can be more effective in dealing with the media.
Illinois Journal of Mathematics, 2009
We study the Cheeger constants of certain infinite families of arithmetic hyperbolic three-manifo... more We study the Cheeger constants of certain infinite families of arithmetic hyperbolic three-manifolds, as well as certain graphs associated to these manifolds. We derive computable bounds on the Cheeger constants, and therefore bounds on the first eigenvalue of the Laplacian, by adapting discrete methods due to Brooks, Perry and Petersen. We then modify probabilistic methods due to Brooks and Zuk
The Electronic Journal of Combinatorics, 2011
Page 1. Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Ri... more Page 1. Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces Dominic Lanphier∗ Department of Mathematics Western Kentucky UniversityBowling Green, KY 42101, USA [email protected] Jason Rosenhouse ...
Illinois Journal of Mathematics, 2009
We study the Cheeger constants of certain infinite families of arithmetic hyperbolic three-manifo... more We study the Cheeger constants of certain infinite families of arithmetic hyperbolic three-manifolds, as well as certain graphs associated to these manifolds. We derive computable bounds on the Cheeger constants, and therefore bounds on the first eigenvalue of the Laplacian, by adapting discrete methods due to Brooks, Perry and Petersen. We then modify probabilistic methods due to Brooks and Zuk
We develop a method for obtaining lower bounds on the Cheeger constants of certain highly connect... more We develop a method for obtaining lower bounds on the Cheeger constants of certain highly connected graphs. We then apply this technique to obtain new lower bounds on the Cheeger constants of two important families of graphs. Finally, we discuss the relevance of our bounds to determining the integrity of these graphs. Let G be a finite, simple graph with
Ars Combinatoria, 2006
The Levi graph of a balanced incomplete block design is the bi- partite graph whose vertices are ... more The Levi graph of a balanced incomplete block design is the bi- partite graph whose vertices are the points and blocks of the design, with each block adjacent to those points it contains. We derive upper and lower bounds on the isoperimetric numbers of such graphs, with particular attention to the special cases of nite projective planes and Hadamard designs.
The Picard group is dened as = SL(2;Z(i)); the ring of 2 2 matrices with Gaussian integer entries... more The Picard group is dened as = SL(2;Z(i)); the ring of 2 2 matrices with Gaussian integer entries and determinant one. We consider certain graphs associated to quotients =( p) where p is a prime congruent to three mod four and ( p) is the congruence subgroup of level p. We prove a decomposition theorem on the ver- tices of these graphs, and use this decomposition to derive upper and lower bounds on their isoperimetric numbers.
Mathematics Magazine, 2009
Discrete Mathematics, 2004
The Platonic graphs πn arise in several contexts, most simply as a quotient of certain Cayley gra... more The Platonic graphs πn arise in several contexts, most simply as a quotient of certain Cayley graphs associated to the projective special linear groups. We show that when n = p is prime, πn can be viewed as a complete multigraph in which each vertex is itself a wheel on n + 1 vertices. We prove a similar structure theorem for the case of an arbitrary prime power. These theorems are then used to obtain new upper bounds on the Cheeger constants of these graphs. These results lead immediatley to similar results for Cayley graphs of the group P SL(2, Zn).
BioScience, 2006
News media coverage of the controversy surrounding recent attempts to insert creationism into pub... more News media coverage of the controversy surrounding recent attempts to insert creationism into public school science curricula-this time in the form of "intelligent design"-has generated miles of copy and hours of television footage. The quality of that reporting varies widely, depending on the media outlet. Often, reporters with no scientific training are assigned to report on evolution-creationism controversies, which inevitably leads to distortions of the relevant science. A misconceived concern for balance frequently results in equal time being accorded to biologists and creationists, creating the illusion of scientific equivalence. At other times, a clear bias toward creationism is revealed, especially on cable television. Focusing mainly on recent treatments, this article analyzes and critiques specific stories, as well as trends and patterns in coverage in newspapers, magazines, and television; it concludes with suggestions of ways in which scientists can be more effective in dealing with the media.
Journal of the London Mathematical Society, 2003
We give estimates for
Uploads
Papers by Jason Rosenhouse