31 research outputs found
Maximal determinants and saturated D-optimal designs of orders 19 and 37
A saturated D-optimal design is a {+1,-1} square matrix of given order with
maximal determinant. We search for saturated D-optimal designs of orders 19 and
37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are
optimal. For order 19 we find all inequivalent saturated D-optimal designs with
maximal determinant, 2^30 x 7^2 x 17, and confirm that the three known designs
comprise a complete set. For order 37 we prove that the maximal determinant is
2^39 x 3^36, and find a sample of inequivalent saturated D-optimal designs. Our
method is an extension of that used by Orrick to resolve the previously
smallest unknown order of 15; and by Chadjipantelis, Kounias and Moyssiadis to
resolve orders 17 and 21. The method is a two-step computation which first
searches for candidate Gram matrices and then attempts to decompose them. Using
a similar method, we also find the complete spectrum of determinant values for
{+1,-1} matrices of order 13.Comment: 28 pages, 4 figure
Analyticity and Integrabiity in the Chiral Potts Model
We study the perturbation theory for the general non-integrable chiral Potts
model depending on two chiral angles and a strength parameter and show how the
analyticity of the ground state energy and correlation functions dramatically
increases when the angles and the strength parameter satisfy the integrability
condition. We further specialize to the superintegrable case and verify that a
sum rule is obeyed.Comment: 31 pages in harvmac including 9 tables, several misprints eliminate
Integrable Lattice Realizations of Conformal Twisted Boundary Conditions
We construct integrable realizations of conformal twisted boundary conditions
for ^sl(2) unitary minimal models on a torus. These conformal field theories
are realized as the continuum scaling limit of critical A-D-E lattice models
with positive spectral parameter. The integrable seam boundary conditions are
labelled by (r,s,\zeta) in (A_{g-2},A_{g-1},\Gamma) where \Gamma is the group
of automorphisms of G and g is the Coxeter number of G. Taking symmetries into
account, these are identified with conformal twisted boundary conditions of
Petkova and Zuber labelled by (a,b,\gamma) in (A_{g-2}xG, A_{g-2}xG,Z_2) and
associated with nodes of the minimal analog of the Ocneanu quantum graph. Our
results are illustrated using the Ising (A_2,A_3) and 3-state Potts (A_4,D_4)
models.Comment: 11 pages, LaTeX. Added some reference
Conference on Best Practices for Managing \u3cem\u3eDaubert\u3c/em\u3e Questions
This article is a transcript of the Philip D. Reed Lecture Series Conference on Best Practices for Managing Daubert Questions, held on October 25, 2019, at Vanderbilt Law School under the sponsorship of the Judicial Conference Advisory Committee on Evidence Rules. The transcript has been lightly edited and represents the panelists’ individual views only and in no way reflects those of their affiliated firms, organizations, law schools, or the judiciary