Since the discovery of cosmic acceleration, modified gravity theories play an
important role in the modern cosmology. In particular, the well-known
F(R)-theories reached great popularity motivated by the easier formalism and by
the prospect...
Lectures on AKSZ Sigma Models for Physicists
April 17, 2012
Physics
Mathematics
High Energy Physics - Theory
Mathematical Physics
Differential Geometry
Mathematical Physics
Symplectic Geometry
This is an introductory review of topological field theories (TFTs) called
AKSZ sigma models. The AKSZ construction is a mathematical formulation for the
construction and analyses of a large class of TFTs, inspired by the
Batalin-Vilkovisky...
Riemannian Metrics and Harmonic Sections of Spinor Bundles
April 15, 2012
Mathematics
Differential Geometry
Functional Analysis
We study the clustering of the lowest non negative eigenvalue of the Dirac
operator on a general Dirac bundle when the metric structure is varied. In the
classical case we show that any closed spin manifold of dimension greater than
or equa...
On Isomorphisms of Grassmann Spaces
April 14, 2012
Mathematics
Algebraic Geometry
We exhibit isomorphisms of Grassmann spaces and their relationship with
collineations and embeddings of the underlying projective spaces....
A Central Limit Theorem for Repeating Patterns
April 12, 2012
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Mathematics
Combinatorics
Probability
We prove a central limit theorem for the length of the longest subsequence of
a random permutation which follows one of a class of repeating patterns. This
class includes every fixed pattern of ups and downs having at least one of
each, suc...
The Necessary and Sufficient Conditions for Representing Lipschitz
Bivariate Functions as a Difference of Two Convex Functions(corrected)
April 8, 2012
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Mathematics
Optimization and Control
Differential Geometry
Optimization and Control
Differential Geometry
In the article the necessary and sufficient conditions for a representation
of Lipschitz function of two variables as a difference of two convex functions
are formulated. An algorithm of this representation is given. The outcome of
this alg...
On the behaviour of \gamma\Log p modulo 1
March 8, 2012
Mathematics
Number Theory
We prove non-trivial lower bounds for sums of type \sum_{p\sim
P}g(\gamma\Log p), where g is a non-negative 2π-periodical function and
γ is a given parameter. As an application we prove that
$\zeta(1+it)^{\pm1}\ll\Log\Log (9+...
A Valuation-Theoretic Approach to The Generalized Jacobian Conjecture
March 8, 2012
Mathematics
Commutative Algebra
Our goal is to settle the following result: {\sf Theorem:} {\it Let R be a
Krull domain domain and let Δ1 and Δ2 be subsets of Ht1(R) such that Δ1∪Δ2=Ht1(R) and $\Delta_1\cap
\Delta_2 = ...
Algorithms for Learning Kernels Based on Centered Alignment
March 2, 2012
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Computer Science
Machine Learning
Artificial Intelligence
This paper presents new and effective algorithms for learning kernels. In
particular, as shown by our empirical results, these algorithms consistently
outperform the so-called uniform combination solution that has proven to be
difficult to ...
Finitude g\'eom\'etrique en g\'eom\'etrie de Hilbert + an
erratum/addendum
February 24, 2012
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Mathematics
Geometric Topology
Group Theory
Metric Geometry
The paper is divided in 2 parts. The first part is the original paper of the
second and third authors arXiv:1202.5442v2. The second part is an
erratum/addendum written in english and concatenated at the end of the former
paper. In the errat...