Publications related to Vertex-transitive graph

Beyond Spectral Gap: The Role of the Topology in Decentralized Learning

Martin Jaggi, Thijs Vogels, Hadrien Hendrikx

In data-parallel optimization of machine learning models, workers collaborate to improve their estimates of the model: more accurate gradients allow them to use larger learning rates and optimize faster. In the decentralized setting, in which workers commu ...

Brookline2023

Asymptotics of Cheeger constants and unitarisability of groups

Nicolas Monod, Maria Gerasimova

Given a group Gamma, we establish a connection between the unitarisability of its uniformly bounded representations and the asymptotic behaviour of the isoperimetric constants of Cayley graphs of Gamma for increasingly large generating sets. The connection ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Masato Mimura

The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...

2019

Exponential extinction time of the contact process on finite graphs

Thomas Mountford, Daniel Rodrigues Valesin, Jean-Christophe Mourrat

We study the extinction time tau of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z, then, uniformly over all trees of degr ...

Elsevier Science Bv2016

Boolean logic optimization in majority-inverter graphs

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù

We present a Boolean logic optimization framework based on Majority-Inverter Graph (MIG). An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. Current MIG optimization is supported by a consistent alge ...

2016

Majority-Inverter Graph: A New Paradigm for Logic Optimization

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù

In this paper, we propose a paradigm shift in representing and optimizing logic by using only majority (MAJ) and inversion (INV) functions as basic operations. We represent logic functions by Majority-Inverter Graph (MIG): a directed acyclic graph c ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Boolean Logic Optimization in Majority-Inverter Graphs

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù

We present a Boolean logic optimization framework based on Majority-Inverter Graph (MIG). An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. Current MIG optimization is supported by a consiste ...

2015

Majority-Inverter Graph for FPGA Synthesis

Giovanni De Micheli, Paolo Ienne, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù, David Novo Bruna, Ana Petkovska

In this paper, we present an FPGA synthesis flow based on Majority-Inverter Graph (MIG). An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. MIG manipulation is supported by a consistent alge ...

2015

Small Spectral Radius And Percolation Constants On Non-Amenable Cayley Graphs

Motivated by the Benjamini-Schramm non-unicity of percolation conjecture we study the following question. For a given finitely generated nonamenable group Gamma, does there exist a generating set S such that the Cayley graph (Gamma, S), without loops and m ...

American Mathematical Society2015

Resting-brain functional connectivity predicted by analytic measures of network communication

Jean-Philippe Thiran, Alessandra Griffa, Patric Hagmann, Olaf Sporns

6 The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structur ...

Natl Acad Sciences2014

Vertex-transitive graph

Beyond Spectral Gap: The Role of the Topology in Decentralized Learning

Asymptotics of Cheeger constants and unitarisability of groups

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Exponential extinction time of the contact process on finite graphs

Boolean logic optimization in majority-inverter graphs

Majority-Inverter Graph: A New Paradigm for Logic Optimization

Boolean Logic Optimization in Majority-Inverter Graphs

Majority-Inverter Graph for FPGA Synthesis

Small Spectral Radius And Percolation Constants On Non-Amenable Cayley Graphs

Resting-brain functional connectivity predicted by analytic measures of network communication

Graph Chatbot

Chat with Graph Search

Exponential extinction time of the contact process on finite graphs

Resting-brain functional connectivity predicted by analytic measures of network communication

Beyond Spectral Gap: The Role of the Topology in Decentralized Learning

Asymptotics of Cheeger constants and unitarisability of groups

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Boolean logic optimization in majority-inverter graphs

Majority-Inverter Graph: A New Paradigm for Logic Optimization

Small Spectral Radius And Percolation Constants On Non-Amenable Cayley Graphs

Boolean Logic Optimization in Majority-Inverter Graphs

Majority-Inverter Graph for FPGA Synthesis