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Clustering with mixtures of log-concave distributions
EM algorithm Log-concave distribution Clustering Normal copula
2015/8/20
The EM algorithm is a popular tool for clustering observations via a parametric mixture model. Two disadvantages of this
approach are that its success depends on the appropriateness of the assumed pa...
THE BACKWARD BEHAVIOR OF THE RICCI AND CROSS CURVATURE FLOWS ON SL(2, R)
BACKWARD BEHAVIOR CROSS CURVATURE FLOWS
2015/8/17
This paper is concerned with properties of maximal solutions of the
Ricci and cross curvature flows on locally homogeneous three-manifolds of type
SL2(R). We prove that, generically, a maximal...
CROSS CURVATURE FLOW ON LOCALLY HOMOGENEOUS THREE-MANIFOLDS (II)
CURVATURE FLOW THREE-MANIFOLDS
2015/8/17
In this paper, we study the positive cross curvature flow on locally
homogeneous 3-manifolds. We describe the long time behavior of these flows. We
combine this with earlier results conc...
BACKWARD RICCI FLOW ON LOCALLY HOMOGENEOUS THREE-MANIFOLDS
THREE-MANIFOLDS LOCALLY HOMOGENEOUS
2015/8/17
In this paper, we study the backward Ricci flow on locally homogeneous
3-manifolds. We describe the long time behavior and show that, typically and after
a proper re-scaling, there is converge...
A NOTE ON STRONGLY SEPARABLE ALGEBRAS
Separable algebras invariants coinvariants coalgebras Hopf algebras
2015/8/14
Let A be an algebra over a field k. If M is an A–bimodule, we let
MA and MA denote respectively the k–spaces of invariants and coinvariants of
M, and 'M : MA
! MA be the natural map. In this note w...
QUADRI-ALGEBRAS
quadri-algebra operad Koszul duality
2015/8/14
We introduce the notion of quadri-algebras. These are associative algebras
for which the multiplication can be decomposed as the sum of four operations
in a certain coherent manner. We present sever...
CANONICAL CHARACTERS ON QUASI-SYMMETRIC FUNCTIONS AND BIVARIATE CATALAN NUMBERS
Hopf algebra character quasi-symmetric function central binomial coefficient
2015/8/14
Every character on a graded connected Hopf algebra decomposes uniquely as
a product of an even character and an odd character [2]. We obtain explicit formulas for
the even and odd parts of the unive...
The peak algebra Pn is a unital subalgebra of the symmetric group algebra,
linearly spanned by sums of permutations with a common set of peaks. By exploiting
the combinatorics of sparse subsets of [...
HOPF MONOIDS IN THE CATEGORY OF SPECIES
Species Hopf monoid Lie monoid antipode Hadamard product
2015/8/14
A Hopf monoid (in Joyal’s category of species) is an algebraic
structure akin to that of a Hopf algebra. We provide a self-contained introduction
to the theory of Hopf monoids in the category of spe...
BUTTERFLY FACTORIZATION
data-sparse matrix butterfly algorithm randomized algorithm matrix factorization operator compression Fourier integral operators special functions
2015/7/14
The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if eit...
The ring of projective invariants of n ordered points on the projective line is one of the most
basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the poin...
Universal covering spaces and fundamental groups in algebraic geometry as schemes
algebraic geometry fundamental groups
2015/7/14
In topology, the notions of the fundamental group
and the universal cover are closely intertwined. By importing
usual notions from topology into the algebraic and arithmetic setting, we construct a ...
THE AFFINE STRATIFICATION NUMBER AND THE MODULI SPACE OF CURVES
AFFINE STRATIFICATION NUMBER MODULI SPACE
2015/7/14
One relevant example (Example 4.9) turns out to be a proper integral variety with no
embeddings in a smooth algebraic space. This one-paragraph construction appears to be
simpler and more elementary...
MURPHY’S LAW IN ALGEBRAIC GEOMETRY: BADLY-BEHAVED DEFORMATION SPACES
LAW IN ALGEBRAIC GEOMETRY DEFORMATION SPACES
2015/7/14
We consider the question: “How bad can the deformation space of an object
be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as possible...
The regularity conclusion in Lemma 1.4 is incorrect (G. Pappas gave a counterexample). Regularity of
X must be assumed as a hypothesis, and then the other conclusions follow (see below; also cf. [CEP...