A conjecture of E. D. Bolker

The maximum numbers A(m, n) of basic feasible solutions of non-degenerate m×n transportation problems are known when n=km+c and c=0, 1 or m-1. Recently the cases c=2 and m-2 have also been settled. In 1972 E. D. Bolker was led to believe that A(m, n) was always of the form A(m, km+c)=(n!/(k!)m) P(m, c, k), where P(m, c, k) is a polynomial in k with integer coefficients and highest term mm-2km-c-1. This conjecture is proved

Review of new physics effects in t-tbar production

Both CDF and DO report a forward-backward asymmetry in t-tbar production that is above the standard model prediction. We review new physics models that can give a large forward backward asymmetry in t-tbar production at the Tevatron and the constraints these models face from searches for dijet resonances and contact interactions, from flavor physics and the t-tbar cross section. Expected signals at the LHC are also reviewed.Comment: 18 pages, 18 figures, 4 tables, invited review for a special "Top and flavour physics in the LHC era" issue of The European Physical Journal C, we invite comments regarding contents of the revie

Long-baseline neutrino oscillation experiments and CP violation in the lepton sector

We discuss possibilities to investigate the effects of CP (and T) violation in the lepton sector in neutrino oscillation experiments. We consider the effects of CP violation in the framework of two schemes of mixing of four massive neutrinos that can accommodate the results of all neutrino oscillation experiments. Using the constraints on the mixing parameters that follow from the results of short-baseline neutrino oscillation experiments, we derive rather strong upper bounds on the effects of CP violation in nu_munu_e transitions in long-baseline neutrino oscillation experiments. We show that the effects of CP violation in nu_munu_tau transitions in long-baseline oscillation experiments can be as large as is allowed by the unitarity of the mixing matrix. The matter effects, which complicate the problem of searching for CP violation in long-baseline experiments, are discussed in detail. We consider the T-odd asymmetries whose measurement could allow to reveal T and CP violation in the lepton sector independently from matter effects.Comment: 31 pages, including 5 figure

High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43596/1/11336_2003_Article_1141.pd