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From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Related publications (41)

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Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Thanh Trung Huynh, Quoc Viet Hung Nguyen, Thành Tâm Nguyên

The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entiti ...

London2023

Capturing Types

Martin Odersky, Aleksander Slawomir Boruch-Gruszecki, Ondrej Lhoták

Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CC

New York2023

From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...

EPFL2022

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Pedestrian typologies - nuanced considerations of urban walking

Vincent Kaufmann, Renate Albrecher

The analyses of urban environments, norms, micro-census and scientific studies reveal a variety of myths about pedestrians. One of them is the dominant representation of the pedestrian: A single person, usually with healthy body and in leisure mode. Pedest ...

2022

Towards a secure and trustworthy imaging with non-fungible tokens

Touradj Ebrahimi, Evgeniy Upenik, Davi Nachtigall Lazzarotto

Non fungible tokens (NFTs) are used to define the ownership of digital assets. More recently, there has been a surge of platforms to auction digital art as well as other digital assets in form of image, video, and audio content of all sorts. Although NFTs ...

2021

The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties, wher ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

To share an event that happened or could have happen on the road in relation to architecture or space in a wider sense. ...

MANSLAB2020

Device and method for sorting biological entities

Francesco Mondada, Norbert Crot, Frank Bonnet

A device for sorting biological entities is disclosed. The device comprises a channel to canalize the biological entities and a selector having slots to accommodate said entities. Means for detecting and analysing an optical parameter of the biological ent ...

2019

Humans are comparison machines: comparing and choosing an item among a set of alternatives (such as objects or concepts) is arguably one of the most natural ways for us to express our preferences and opinions. In many applications, the analysis of data con ...

EPFL2018