Design and develop a MOS magnetic memory Final report, 11 Mar. - 11 Sep. 1966

Interface problems between plated wire magnetic memory and MO

Density of States of Quantum Spin Systems from Isotropic Entanglement

We propose a method which we call "Isotropic Entanglement" (IE), that predicts the eigenvalue distribution of quantum many body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.Comment: 4+ pages, content is as in the published versio

Zeta Polynomials and the Möbius Function

Using the theory of zeta polynomials, chain generalizations of well-known Möbius function identities are obtained. The proofs of these identities are combinatorial, and the Möbius function identities follows as corollaries

Multichains, non-crossing partitions and trees

AbstractBijections are presented between certain classes of trees and multichains in non-crossing partition lattices

Is Groton the Next \u3ci\u3eEvenwel\u3c/i\u3e?

In Evenwel v. Abbott the Supreme Court left open the question of whether states could employ population measures other than total population as a basis for drawing representative districts so as to meet the requirement of one person, one vote (OPOV). It was thought that there was little prospect of resolving this question soon as no appropriate instances of such behavior were known. That belief was mistaken. In this Essay I report on the Town of Groton, Connecticut, which uses registered voter data to apportion seats in its Representative Town Meeting and has done so since its incorporation in 1957. The resulting apportionment arguably meets the requirements of OPOV as applied to registered voter data but badly fails if total population is employed. Thus, it would make a good test case to resolve some of the open questions in Evenwel

The Law and Large Numbers. Book Review of Political Numeracy: Mathematical Perspectives on Our Chaotic Constitution. by Michael I. Meyerson

Book review of Political numeracy: mathematical perspectives on our chaotic constitution. By Michael I. Meyerson. W. W. Norton and Company. 2002. Pp. 9, 287

The Dimension of the Supreme Court

In a paper published in the Proceedings of the National Academy of Sciences, Lawrence Sirovich introduced two novel mathematical techniques to study patterns in recent Supreme Court decisions. One of these methods, information theory, has never been applied previously. The other method, singular value decomposition, is closely related to other methods that have previously been employed. In this paper I give an explication of these two methods and evaluate their use in the context of understanding the Supreme Court. I conclude that information theory holds some promise for furthering our understanding but singular value decomposition, as applied by Sirovich, is a less appropriate methodology