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EigenPrism:Inference for High-Dimensional Signal-to-Noise Ratios
EigenPrism High-Dimensional Signal Noise Ratios
2015/6/17
Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional (p > n) regression estimator, (2) the linear...
Computing Multidimensional Residues
The coefficient of polynomial algebra function rational dependence coefficient
2014/12/29
Given n polynomials in n variables with a finite number of complex roots, for any of their roots there is a local residue operator assigning a complex number to any polynomial. This is an algebraic, b...
The Spinor Representation of Minimal Surfaces
Screw die space the projective plane the average curvature functions
2014/12/29
The spinor representation is developed and used to investigate minimal surfaces in R^3 with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are deter...
ON THE LOCUS OF HODGE CLASSES
The singular complex algebraic varieties polarization projection parameters trajectory
2014/12/29
Let S be a nonsingular complex algebraic variety and V a polarized variation of Hodge structure of weight 2p with polarization form Q. Given an integer K, let S(K) be the space of pairs (s, u) with s ...
Dressing orbits of harmonic maps
Mapping equation of Riemann surface mapping Riemannian symmetric Spaces soliton theory
2014/12/29
We study the harmonic map equations for maps of a Riemann surface into a Riemannian symmetric space of compact type from the point of view of soliton theory. There is a well-known dressing action of a...
Isometric immersions of space forms and soliton theory
Isometric immersed space form the soliton theory
2014/12/29
Isometric immersions of space forms and soliton theory.
Curved flats in symmetric spaces.
PERVERSE SHEAVES ON LOOP GRASSMANNIANS AND LANGLANDS DUALITY
Abnormal bundle of circulation LANGLANDS duality
2014/12/29
PERVERSE SHEAVES ON LOOP GRASSMANNIANS AND LANGLANDS DUALITY.
The Singular Supports of IC Sheaves on Quasimaps' Spaces are Irreducible
IC bundle Quasimaps space singular
2014/12/29
The Singular Supports of IC Sheaves on Quasimaps' Spaces are Irreducible.
Resultants, Jacobians and residues are basic invariants of multivariate polynomial systems. We examine their interrelations in the context of toric geometry. The global residue in the torus, studied b...
We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X.We first prove a global transformation law for toric residues. When the fan of the t...
Curved flats and isothermic surfaces.
Bonnet pairs and isothermic surfaces
Four yuan function the theory of differential geometry quaternion Riemann surface figure maps
2014/12/29
In this note we classify all Bonnet pairs on a simply connected domain. Our main intent was to apply what we call a quaternionic function theory to a concrete problem in differential geometry. The ide...
Rank 2 Integrable Systems of Prym Varieties.
Semiinfinite Flags. I. Case of Global Curve P^1
Half infinite flags curve around the world
2014/12/29
Semiinfinite Flags. I. Case of Global Curve P^1.