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Multiscale Geometric Analysis for 3-D Catalogues
laments large scale structures galaxy distribution
2015/8/21
We have developed tools for analysis of 3-D volumetric data which allow sensitive characterizations of point
clouds containing ˉlamentary structures. Our approach involves multiscale X-ray transforms...
Higher Criticism for Detecting Sparse Heterogeneous Mixtures
Multiple Comparsions Combining Many p-values
2015/8/21
Higher Criticism, or second-level significance testing, is a multiple comparisons concept
mentioned in passing by Tukey (1976). It concerns a situation where there are many independent tests of...
COUNTING FACES OF RANDOMLY-PROJECTED POLYTOPES WHEN THE PROJECTION RADICALLY LOWERS DIMENSION
RANDOMLY-PROJECTED RADICALLY LOWERS DIMENSION
2015/8/21
The modern trend in statistics and probability is to consider the case where both
the number of dimensions d and the sample size n are large [19, 21]. In that case, the
intuition fostered by the cla...
Neighborliness of Randomly-Projected Simplices in High Dimensions
Neighborly Polytopes Convex Hull of Gaussian Sample
2015/8/21
Let A be a d by n matrix, d < n. Let T = T
n−1 be the standard regular simplex in R
n
.
We count the faces of the projected simplex AT in the case where the projection is random,
the dimens...
The LASSO risk: asymptotic results and real world examples
Coefficient vector linear observation construct sparse the lasso matrix sequence
2015/8/21
We consider the problem of learning a coefficient vector x0 ∈ RN from noisy linear observation y = Ax0 + w ∈ Rn. In many contexts (ranging from model
selection to image processing) it is desirable to...
Optimal mixture weights in multiple importance sampling
multiple importance sampling mixture
2015/8/21
In multiple importance sampling we combine samples from a nite list
of proposal distributions. When those proposal distributions are used to
create control variates, it is possible (Owen and Zhou, ...
Selection and Estimation for Large-Scale Simultaneous Inference
Large-Scale Simultaneous Inference Selection
2015/8/20
Modern scientific technology is providing a new class of simultaneous inference
problems for the applied statistician, where there are hundreds or thousands or even
more hypothesis tests to co...
DIFFERENTIAL HARNACK ESTIMATES FOR TIME-DEPENDENT HEAT EQUATIONS WITH POTENTIALS
EQUATIONS WITH POTENTIALS DIFFERENTIAL HARNACK
2015/8/17
In this paper, we prove a differential Harnack inequality for positive
solutions of time-dependent heat equations with potentials. We also prove a gradient
estimate for the positive solution o...
FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE RICCI FLOW
GEOMETRIC OPERATORS UNDER FLOW
2015/8/17
In this paper, we prove that the first eigenvalues of
−∆ + cR (c ≥
1
4
) is nondecreasing under the Ricci flow. We also
prove the monotonicity under the normalized Ricci &...
CROSS CURVATURE FLOW ON LOCALLY HOMOGENOUS THREE-MANIFOLDS (I)
HOMOGENOUS THREE-MANIFOLDS CURVATURE FLOW
2015/8/17
Chow and Hamilton introduced the cross curvature flow on closed 3-
manifolds with negative or positive sectional curvature. In this paper, we study
the negative cross curvature flow in t...
Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Positive Curvature Operator Shrinking Ricci Solitons
2015/8/17
In this paper, we first derive several identities on a compact shrinking Ricci
soliton. We then show that a compact gradient shrinking soliton must be
Einstein, if it admits a Riemannian metri...
Spherical Unitary dual for quasisplit real groups
quasisplit real groups Spherical Unitary
2015/8/17
G is the real points of a linear connected reductive group.
- g0 := Lie(G), Cartan involution, g0 = k0 + s0, g := (g0)C, K
maximal compact subgroup, g = k + s,
- P = MAN minimal parabolic subgrou...
SPHERICAL UNITARY DUAL FOR COMPLEX CLASSICAL GROUPS
CLASSICAL GROUPS SPHERICAL UNITARY DUAL
2015/8/17
The full unitary dual for the complex classical groups viewed as real Lie
groups is computed in [B1]. This was close to 20 years ago. Since then there
have been many advances, but the general proble...
SPHERICAL UNITARY REPRESENTATIONS FOR SPLIT REAL AND P-ADIC GROUPS
UNITARY REPRESENTATIONS P-ADIC GROUPS
2015/8/17
1.1. Positive de nite functions. We start with the classical notion of
positive de nite functions.
De nition. A continuous function f : R ! C is called positive de nite if
it satis es
(1...
THE ASSOCIATIVE OPERAD AND THE WEAK ORDER ON THE SYMMETRIC GROUPS
Hopf algebr factorizable inverse monoid uniform block permutation
2015/8/14
We introduce the Hopf algebra of uniform block permutations and show that
it is self-dual, free, and cofree. These results are closely related to the fact that uniform
block permutations form a fact...