Publications related to Unimodular lattice

Mean value theorems for collections of lattices with a prescribed group of symmetries

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

High-Resolution Modeling Without Computation Slowdown for PETALE in CROCUS

Andreas Pautz, Vincent Pierre Lamirand, Thomas Jean-François Ligonnet, Axel Guy Marie Laureau

In a collaboration between Ecole Polytechnique Fédérale de Lausanne (EPFL) and CEA, in the fall of 2020, the experimental Programme d’Étude en Transmission de l’Acier Lourd et ses Eléments (PETALE) was successfully carried out in the CROCUS reactor of EPFL ...

2024

Nonlinear dynamics and Kerr frequency comb formation in lattices of coupled microresonators

Tobias Kippenberg, Aleksandr Tusnin, Alexey Tikan, Kenichi Komagata

Recently, substantial progress has been made in the understanding of microresonators frequency combs based on dissipative Kerr solitons (DKSs). However, most of the studies have focused on the single-resonator level. Coupled resonator systems can open new ...

Berlin2023

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Vlad Serban, Nihar Prakash Gargava

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Phase of Topological Lattice with Leaky Guided Mode Resonance

Kirsten Emilie Moselund, Chang Won Lee

Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk-edge correspondence and symmetry-related to ...

Basel2023

Direct high-temperature growth of single-crystalline GaN on ScAlMgO4 substrates by metalorganic chemical vapor deposition

Elison de Nazareth Matioli, Alessandro Floriduz

In this note, we demonstrate direct high-temperature growth of single-crystalline GaN on c-plane ScAlMgO4 substrates by metalorganic chemical vapor deposition, without using low-temperature buffers. We found that a trimethylaluminium preflow was crucial to ...

IOP Publishing Ltd2022

Almost impossible E_8 and Leech lattices

Maryna Viazovska

We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...

2021

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

SPRINGER HEIDELBERG2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio & Voulgaris (2010) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus may need exponen ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

Unimodular lattice

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Mean value theorems for collections of lattices with a prescribed group of symmetries

High-Resolution Modeling Without Computation Slowdown for PETALE in CROCUS

Nonlinear dynamics and Kerr frequency comb formation in lattices of coupled microresonators

Moments of the number of points in a bounded set for number field lattices

Phase of Topological Lattice with Leaky Guided Mode Resonance

Direct high-temperature growth of single-crystalline GaN on ScAlMgO4 substrates by metalorganic chemical vapor deposition

Almost impossible E_8 and Leech lattices

On compact representations of Voronoi cells of lattices

New Results in Integer and Lattice Programming

On compact representations of Voronoi cells of lattices

Mean value theorems for collections of lattices with a prescribed group of symmetries

Moments of the number of points in a bounded set for number field lattices

High-Resolution Modeling Without Computation Slowdown for PETALE in CROCUS

Nonlinear dynamics and Kerr frequency comb formation in lattices of coupled microresonators

Almost impossible E_8 and Leech lattices

New Results in Integer and Lattice Programming

On compact representations of Voronoi cells of lattices

Phase of Topological Lattice with Leaky Guided Mode Resonance

On compact representations of Voronoi cells of lattices

Direct high-temperature growth of single-crystalline GaN on ScAlMgO4 substrates by metalorganic chemical vapor deposition