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...
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...
Zero Noise Selections of Multidimensional Peano Phenomena
Some Connections Between The Arithmetic and The Geometry of Lipschitz
Integers
January 27, 2012
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Mathematics
Number Theory
Some relationships between the arithmetic and the geometry of Lipschitz and
Hurwitz integers are presented. In particular, it is shown that the (ternary)
vector product of a Lipschitz integer α with two other Lipschitz
integers, both...
Identification of transformer overload and new energy planning for
enterprises based on load forecasting
January 11, 2012
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Physics
Mathematics
Mathematical Physics
Mathematical Physics
Mathematical Physics
Mathematical Physics
The new energy system constructed by energy storage and photovoltaic power
generation system can effectively solve the problem of transformer overload
operation in some enterprises. It can not only reduce the cost of electricity,
but also r...
The Fundamental Theorem of Phyllotaxis revisited
January 8, 2012
Quantitative Biology
Tissues and Organs
Jean's `Fundamental Theorem of Phyllotaxis' (\emph{Phyllotaxis: a systematic
study in Plant Morphogenesis}, CUP 1994) describes the relationship between the
count numbers of observed spirals in cylindrical lattices and the horizontal
angle ...
An explicit version of Shimura's reciprocity law for Siegel modular
functions
December 29, 2011
Mathematics
Number Theory
We give an explicit version of Shimura's reciprocity law for singular values
of Siegel modular functions. We use this to construct the first examples of
class invariants of quartic CM fields that are smaller than Igusa invariants.
Our state...