We construct the Nahm transform for Higgs bundles over a Riemann surface of genus at least 2 as hyperholomorphic connections on the total space of the tangent bundle of its dual Jacobian. 2000 MSC: 53C07, 53C26

We study extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of compact genus two Riemann surfaces. By a combination of analytical and numerical methods we identify four non-degenerate critical points of this function and compute the signature of the Hessian at these points. The curve with the maximal number of automorphisms (the Burnside curve) tur...

We propose a flexible statistical model for high-dimensional quantitative data on a hypercube. Our model, called the structural gradient model (SGM), is based on a one-to-one map on the hypercube that is a solution for an optimal transport problem. As we show with many examples, SGM can describe various dependence structures including correlation and heteroscedasticity. The maximum likelihood e...

This paper discusses four techniques to successfully track two closely-spaced and unresolved targets using monopulse radar measurements, the quality of such tracking being a determinant of successful detection of target spawn. It explores statistical estimation techniques based on the maximum likelihood criterion and Gibbs sampling, and addresses concerns about the accuracy of the measurements ...

Large numbers of branched muscle fibers occur in the freely grafted rat extensor digitorum longus muscle. The ratio of branched/non-branched muscle fibers in grafts is much higher in old (24 months) than in young (4 months) host rats. Crossage transplants show that the proportion of branched muscle fibers is related to the age of the grafted muscle and not to the age of the host. This is in con...

The strongly correlated regime of the crossover from Bardeen-Cooper-Schrieffer pairing to Bose-Einstein condensation can be realized by diluting a system of two-component fermions with a short-range attractive interaction. We investigate this system via a novel continuous-space-time diagrammatic determinant Monte Carlo method and determine the universal curve Tc/epsilonF for the transition temp...

A new class of robust estimates for vector autoregressive processes is proposed. The autoregressive coefficients and the covariance matrix of the innovations are estimated simultaneously by minimizing the determinant of the covariance matrix estimate, subject to a constraint on a robust scale of the Mahalanobis norms of the innovation residuals. By choosing as robust scale a τ− estimate, the re...

Rousseeuw’s minimum covariance determinant (MCD) method is a highly robust estimator of multivariate mean and covariance. In practice, the MCD covariance estimator may be singular. However, a nonsingular covariance estimator is required to calculate the Mahalanobis distance. In order to fix this singular problem, we propose an improved version of the MCD estimator, which is a combination of the...

We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Problem { the problem of choosing the s s principal submatrix with maximal determinant from a given n n positive deenite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous imple...