Nonexistence of generalized bent functions and the quadratic norm form
equations
April 4, 2018
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Computer Science
Mathematics
Information Theory
Information Theory
Number Theory
Information Theory
Information Theory
Number Theory
We present a new result on the nonexistence of generalized bent functions
(GBFs)from (Z/tZ)^n to Z/tZ (called type [n, t]) for a large class. Assume p is
an odd prime number. By showing certain quadratic norm form equations having no
integr...
Average non-vanishing of Dirichlet L-functions at the central point
April 4, 2018
Mathematics
Number Theory
The Generalized Riemann Hypothesis implies that at least 50% of the central
values L(21,χ) are non-vanishing as χ ranges
over primitive characters modulo q. We show that one may unconditionally go
beyond GR...
Distributed Online Optimization for Multi-Agent Optimal Transport
April 4, 2018
|
Mathematics
Optimization and Control
We propose a scalable, distributed algorithm for the optimal transport of
large-scale multi-agent systems. We formulate the problem as one of steering
the collective towards a target probability measure while minimizing the total
cost of tr...
An investigation of the non-trivial zeros of the Riemann zeta function
April 4, 2018
Mathematics
General Mathematics
While many zeros of the Riemann zeta function are located on the critical
line ℜ(s)=1/2, the non-existence of zeros in the remaining part of the
critical strip ℜ(s)∈]0,1[ is the main scope to be proven for the
Riemann hypoth...
Spectral Triples on Thermodynamic Formalism and Dixmier Trace
Representations of Gibbs: theory and examples
April 4, 2018
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Mathematics
Physics
Dynamical Systems
Statistical Mechanics
Mathematical Physics
Functional Analysis
Mathematical Physics
In this paper we study spectral triples and non-commutative expectations
associated to expanding and weakly expanding maps. In order to do so, we
generalize the Perron-Frobenius-Ruelle theorem and obtain a polynomial decay of
the operator, ...
The noise barrier and the large signal bias of the Lasso and other
convex estimators
April 3, 2018
|
Mathematics
Statistics
Statistics Theory
Statistics Theory
Statistics Theory
Statistics Theory
Convex estimators such as the Lasso, the matrix Lasso and the group Lasso
have been studied extensively in the last two decades, demonstrating great
success in both theory and practice. Two quantities are introduced, the noise
barrier and t...
A complete description of the asymptotic behavior at infinity of
positive radial solutions to Δ2u=uα in Rn
March 30, 2018
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Mathematics
Analysis of PDEs
We consider the biharmonic equation Δ2u=uα in Rn
with n⩾1. It was proved that this equation has a positive classical
solution if, and only if, either α⩽1 with n⩾1 or
$\alp...
Weak contractions via λ-sequences
March 30, 2018
|
Mathematics
General Topology
In this note, we discuss common fixed point for a family of self mapping
defined on a metric type space and satisfying a weakly contractive condition.
In our development, we make use of the λ-sequence approach and also of
a certain ...
A Novel Framework for Online Supervised Learning with Feature Selection
March 30, 2018
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Statistics
Computer Science
Machine Learning
Machine Learning
Current online learning methods suffer issues such as lower convergence rates
and limited capability to select important features compared to their offline
counterparts. In this paper, a novel framework for online learning based on
running ...
L\'evy Area Analysis and Parameter Estimation for fOU Processes via
Non-Geometric Rough Path Theory
March 29, 2018
|
Mathematics
Statistics
Probability
Statistics Theory
Statistics Theory
This paper addresses the estimation problem of an unknown drift parameter
matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional
setting. To tackle this problem, we propose a novel approach based on rough
path theory that...