Research articles

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

\Re(s)=1/2

, the non-existence of zeros in the remaining part of the critical strip

\Re(s) \in \, ]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

| | |

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

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 $\Delta^2 u = u^\alpha$ in $\mathbf R^n$

March 30, 2018

| |

Mathematics

Analysis of PDEs

We consider the biharmonic equation

\Delta^2 u = u^\alpha

\mathbf R^n

with

n \geqslant 1

. It was proved that this equation has a positive classical solution if, and only if, either

\alpha \leqslant 1

with

n \geqslant 1

or $\alp...

Weak contractions via $\lambda$ -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

\lambda

-sequence approach and also of a certain ...

A Novel Framework for Online Supervised Learning with Feature Selection

March 30, 2018

| | |

Statistics

Computer Science

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

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...

On tensors of factorizable quantum channels with the completely depolarizing channel

March 28, 2018

Mathematics

Physics

Operator Algebras

Mathematical Physics

In this paper, we obtain results for factorizability of quantum channels. Firstly, we prove that if a tensor

T\otimes S_k

of a quantum channel

T

M_n(\mathbb{C})

with the completely depolarizing channel

S_k

is written as a convex ...

On Difference-of-SOS and Difference-of-Convex-SOS Decompositions for Polynomials

March 27, 2018

| |

Mathematics

Optimization and Control

In this article, we are interested in developing polynomial decomposition techniques based on sums-of-squares (SOS), namely the difference-of-sums-of-squares (D-SOS) and the difference-of-convex-sums-of-squares (DC-SOS). In particular, the ...

Derivation of the Invariant Free-Energy Landscape Based on Langevin Dynamics

March 23, 2018

Physics

Statistical Mechanics

Conventionally defined free-energy landscape (FEL) exhibits unphysical dependence on the choice of reaction coordinates and hence lacks universal predictive ability. We here show that three physically plausible requirements uniquely determi...

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

\Re(s)=1/2

, the non-existence of zeros in the remaining part of the critical strip

\Re(s) \in \, ]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

| | |

Mathematics

Physics

Dynamical Systems

Statistical Mechanics

Mathematical Physics

Functional Analysis

Mathematical Physics

The noise barrier and the large signal bias of the Lasso and other convex estimators

April 3, 2018

Mathematics

Statistics

Statistics Theory

A complete description of the asymptotic behavior at infinity of positive radial solutions to $\Delta^2 u = u^\alpha$ in $\mathbf R^n$

March 30, 2018

| |

Mathematics

Analysis of PDEs

We consider the biharmonic equation

\Delta^2 u = u^\alpha

\mathbf R^n

with

n \geqslant 1

. It was proved that this equation has a positive classical solution if, and only if, either

\alpha \leqslant 1

with

n \geqslant 1

or $\alp...

Weak contractions via $\lambda$ -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

\lambda

-sequence approach and also of a certain ...

A Novel Framework for Online Supervised Learning with Feature Selection

March 30, 2018

| | |

Statistics

Computer Science

Machine Learning

L\'evy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory

March 29, 2018

Mathematics

Statistics

Probability

Statistics Theory

On tensors of factorizable quantum channels with the completely depolarizing channel

March 28, 2018

Mathematics

Physics

Operator Algebras

Mathematical Physics

In this paper, we obtain results for factorizability of quantum channels. Firstly, we prove that if a tensor

T\otimes S_k

of a quantum channel

T

M_n(\mathbb{C})

with the completely depolarizing channel

S_k

is written as a convex ...

On Difference-of-SOS and Difference-of-Convex-SOS Decompositions for Polynomials

March 27, 2018

| |

Mathematics

Optimization and Control

Derivation of the Invariant Free-Energy Landscape Based on Langevin Dynamics

March 23, 2018

Physics

Statistical Mechanics

An investigation of the non-trivial zeros of the Riemann zeta function

Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

The noise barrier and the large signal bias of the Lasso and other convex estimators

A complete description of the asymptotic behavior at infinity of positive radial solutions to Δ2u=uα\Delta^2 u = u^\alphaΔ2u=uα in Rn\mathbf R^nRn

Weak contractions via λ\lambdaλ-sequences

A Novel Framework for Online Supervised Learning with Feature Selection

L\'evy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory

On tensors of factorizable quantum channels with the completely depolarizing channel

On Difference-of-SOS and Difference-of-Convex-SOS Decompositions for Polynomials

Derivation of the Invariant Free-Energy Landscape Based on Langevin Dynamics

An investigation of the non-trivial zeros of the Riemann zeta function

Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

The noise barrier and the large signal bias of the Lasso and other convex estimators

A complete description of the asymptotic behavior at infinity of positive radial solutions to Δ2u=uα\Delta^2 u = u^\alphaΔ2u=uα in Rn\mathbf R^nRn

Weak contractions via λ\lambdaλ-sequences

A Novel Framework for Online Supervised Learning with Feature Selection

L\'evy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory

On tensors of factorizable quantum channels with the completely depolarizing channel

On Difference-of-SOS and Difference-of-Convex-SOS Decompositions for Polynomials

Derivation of the Invariant Free-Energy Landscape Based on Langevin Dynamics

A complete description of the asymptotic behavior at infinity of positive radial solutions to $\Delta^2 u = u^\alpha$ in $\mathbf R^n$

Weak contractions via $\lambda$ -sequences

A complete description of the asymptotic behavior at infinity of positive radial solutions to $\Delta^2 u = u^\alpha$ in $\mathbf R^n$

Weak contractions via $\lambda$ -sequences