Publications related to Algebraic number field

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

MATHICSE Technical Report : A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems

Alfio Quarteroni, Andrea Manzoni

When using Newton iterations to solve nonlinear parametrized PDEs in the context of Reduced Basis (RB)methods, the assembling of the RB arrays in the online stage depends in principle on the high-fidelityapproximation. This task is even more challenging wh ...

MATHICSE2016

Apparent compensation mechanisms in relatives of schizophrenia patients in visual backward masking

Michael Herzog, Maya Roinishvili, Patricia Figueiredo, Janir Nuno Ramos Antunes Da Cruz

Visual backward masking (VBM) is strongly deteriorated in schizophrenia patients. VBM is a potential endophenotype of schizophrenia reflecting the genetic underpinnings of the disease (Chkonia et al., 2010). Masking deficits are highly correlated with redu ...

2016

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

Alfio Quarteroni, Paolo Pacciarini

We propose and analyse a new discontinuous reduced basis element method for the approximation of parametrized elliptic PDEs in partitioned domains. The method is built upon an offline stage (parameter independent) and an online (parameter dependent) one. I ...

Edp Sciences S A2016

Angular distortive matrices of phase transitions in the fcc-bcc-hcp system

Cyril Cayron

This work generalizes the one-step model previously developed on fcc-bcc martensitic transformations to the larger family of phase transitions in the fcc-bcc-hcp system. The angular distortive matrices are calculated for the bcc-fcc, bcc-hcp and fcc-hcp tr ...

Elsevier2016

MATHICSE Technical Report : Multilevel tensor approximation of PDEs with random data

Daniel Kressner, Jonas Ballani, Michael Dieter Peters

In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a deterministic parame ...

MATHICSE2016

Upper bounds for Euclidean minima of abelian number fields

Eva Bayer Fluckiger, Piotr Aleksander Maciak

Le but de cet article est de donner des bornes supérieures pour les minima euclidiens de corps abéliens, en particulier dans le cas des corps abéliens de conducteurs des puissances de nombres premiers. ...

2015

On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For

q

a prime power, the discrete logarithm problem (DLP) in

\mathbb{F}_q

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer

x

such that

g^x = h

. We present an algorithm for computing discrete log ...

2015

CM values of higher Green's functions and regularized Petersson products

Maryna Viazovska

Higher Green functions are real-valued functions of two variables on the upper half-plane, which are bi-invariant under the action of a congruence subgroup, have a logarithmic singularity along the diagonal, and satisfy the equation f = k(1−k) f ; here i ...

Cambridge UP2015

Algebraic number field

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ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Inhomogeneous minima of mixed signature lattices

MATHICSE Technical Report : A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems

Apparent compensation mechanisms in relatives of schizophrenia patients in visual backward masking

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

Angular distortive matrices of phase transitions in the fcc-bcc-hcp system

MATHICSE Technical Report : Multilevel tensor approximation of PDEs with random data

Upper bounds for Euclidean minima of abelian number fields

On the discrete logarithm problem in finite fields of fixed characteristic

CM values of higher Green's functions and regularized Petersson products

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Inhomogeneous minima of mixed signature lattices

Apparent compensation mechanisms in relatives of schizophrenia patients in visual backward masking

MATHICSE Technical Report : A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

Angular distortive matrices of phase transitions in the fcc-bcc-hcp system

Upper bounds for Euclidean minima of abelian number fields

MATHICSE Technical Report : Multilevel tensor approximation of PDEs with random data

On the discrete logarithm problem in finite fields of fixed characteristic

CM values of higher Green's functions and regularized Petersson products