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The Range of a Random Walk on a Comb

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Global and Local Uncertainty Principles for Signals on Graphs

Pierre Vandergheynst, Nathanaël Perraudin, Benjamin Ricaud, David Shuman

Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph ...

2018

On Simplices in Diameter Graphs in R-4

Andrei Kupavskii

A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...

Maik Nauka/Interperiodica/Springer2017

Linker call graph with full Dotty support

Nicolas Alexander Stucki

This project consisted in bringing the linker call graph up to date with dotty/master, restructure the code, make it support the full Scala language and make it support calls to Java code. Also implemented dead code elimination of unreachable methods based ...

2017

A graph signal filtering-based approach for detection of different edge types on airborne lidar data

Elif Vural, Eda Bayram

Airborne Laser Scanning is a well-known remote sensing technology, which provides a dense and highly accurate, yet unorganized point cloud of earth surface. During the last decade, extracting information from the data generated by airborne LiDAR systems ha ...

2017

Diverse M-Best Solutions by Dynamic Programming

Michaël Unser, Virginie Sophie Uhlmann

Many computer vision pipelines involve dynamic programming primitives such as finding a shortest path or the minimum energy solution in a tree-shaped probabilistic graphical model. In such cases, extracting not merely the best, but the set of M-best soluti ...

Springer2017

Scaling a Reliable Distributed System

Alexandre David Olivier Maurer

We consider the problem of reliably connecting an arbitrarily large set of computers (nodes) with communication channels. Reliability means here the ability, for any two nodes, to remain connected (i.e., their ability to communicate) with probability at le ...

LPD EPFL2016

Assembling a Network out of Ambiguous Patches

Matthias Grossglauser, Lyudmila Yartseva, Jefferson Elbert Simões

Many graph mining and network analysis problems rely on the availability of the full network over a set of nodes. But inferring a full network is sometimes non-trivial if the raw data is in the form of many small {\em patches} or subgraphs, of the true net ...

2016

Disjoint edges in topological graphs and the tangled-thrackle conjecture

Andres Jacinto Ruiz Vargas

It is shown that fora constant t is an element of N, every simple topological graph on n vertices has 0(n) edges if the graph has no two sets of t edges such that every edge in one set is disjoint from all edges of the other set (i.e., the complement of th ...

Academic Press Ltd- Elsevier Science Ltd2016

Simple topological graphs

Andres Jacinto Ruiz Vargas

This thesis is devoted to the understanding of topological graphs. We consider the following four problems: 1. A \emph{simple topological graph} is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any t ...

EPFL2016

Deconvolution of Gaussian Random Fields using the Graph Fourier Transform

Matthieu Martin Jean-André Simeoni

Real-life acquisition systems are fundamentally limited in their ability to reproduce point sources. For example, a point source object, a star say, observed with an optical telescope is blurred by the imperfect lenses composing the system. Mathematically, ...

2016