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@book{oudot_persistence_2015,
location = {Providence, Rhode Island},
title = {Persistence theory: from quiver representations to data analysis},
isbn = {978-1-4704-2545-6},
series = {Mathematical surveys and monographs},
shorttitle = {Persistence theory},
pagetotal = {218},
number = {volume 209},
publisher = {American Mathematical Society},
author = {Oudot, Steve Y.},
date = {2015},
keywords = {Algebraic topology, Algebraic topology -- Applied homological algebra and category theory -- Simplicial sets and complexes, Associative rings and algebras -- Representation theory of rings and algebras -- Representations of quivers and partially ordered sets, Computer science -- Computing methodologies and applications -- Computer graphics; computational geometry, Homology theory, Statistics -- Data analysis},
file = {Steve_Oudot_Persistence_Theory.pdf:/home/dimitri/Zotero/storage/ALZW577G/Steve_Oudot_Persistence_Theory.pdf:application/pdf}
}
@article{carlsson_topology_2009,
title = {Topology and data},
volume = {46},
issn = {0273-0979},
url = {http://www.ams.org/journal-getitem?pii=S0273-0979-09-01249-X},
doi = {10.1090/S0273-0979-09-01249-X},
pages = {255--308},
number = {2},
journaltitle = {Bulletin of the American Mathematical Society},
author = {Carlsson, Gunnar},
urldate = {2017-11-03},
date = {2009-01-29},
langid = {english},
file = {carlsson2009.pdf:/home/dimitri/Zotero/storage/WYT52FA5/carlsson2009.pdf:application/pdf}
}
@article{chazal_introduction_2017,
title = {An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists},
shorttitle = {An introduction to Topological Data Analysis},
journaltitle = {{arXiv} preprint {arXiv}:1710.04019},
author = {Chazal, Frédéric and Michel, Bertrand},
date = {2017},
file = {chazal2017.pdf:/home/dimitri/Zotero/storage/CH8YWVM3/chazal2017.pdf:application/pdf}
}
@article{xu_hierarchical_2017,
title = {Hierarchical Segmentation Using Tree-Based Shape Spaces},
volume = {39},
issn = {0162-8828, 2160-9292},
url = {http://ieeexplore.ieee.org/document/7452658/},
doi = {10.1109/TPAMI.2016.2554550},
pages = {457--469},
number = {3},
journaltitle = {{IEEE} Transactions on Pattern Analysis and Machine Intelligence},
author = {Xu, Yongchao and Carlinet, Edwin and Geraud, Thierry and Najman, Laurent},
urldate = {2017-11-03},
date = {2017-03-01},
file = {xu2016.pdf:/home/dimitri/Zotero/storage/X49E35AC/xu2016.pdf:application/pdf}
}
@article{tierny_generalized_2012,
title = {Generalized topological simplification of scalar fields on surfaces},
volume = {18},
pages = {2005--2013},
number = {12},
journaltitle = {{IEEE} transactions on visualization and computer graphics},
author = {Tierny, Julien and Pascucci, Valerio},
date = {2012},
file = {tierny2012.pdf:/home/dimitri/Zotero/storage/ID96MTE2/tierny2012.pdf:application/pdf}
}
@article{tierny_loop_2009,
title = {Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees},
volume = {15},
shorttitle = {Loop surgery for volumetric meshes},
number = {6},
journaltitle = {{IEEE} Transactions on Visualization and Computer Graphics},
author = {Tierny, Julien and Gyulassy, Attila and Simon, Eddie and Pascucci, Valerio},
date = {2009},
file = {tierny2009.pdf:/home/dimitri/Zotero/storage/9VGB22UH/tierny2009.pdf:application/pdf}
}
@inproceedings{monasse_scale-space_1999,
title = {Scale-space from a level lines tree},
volume = {99},
pages = {175--186},
booktitle = {Scale-Space},
publisher = {Springer},
author = {Monasse, Pascal and Guichard, Frédéric},
date = {1999},
file = {Scale-Space_from_a_Level_Lines_Tree.pdf:/home/dimitri/Zotero/storage/GXHUMD2G/Scale-Space_from_a_Level_Lines_Tree.pdf:application/pdf}
}
@article{robins_theory_2011,
title = {Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images},
volume = {33},
issn = {0162-8828},
url = {http://ieeexplore.ieee.org/document/5766002/},
doi = {10.1109/TPAMI.2011.95},
pages = {1646--1658},
number = {8},
journaltitle = {{IEEE} Transactions on Pattern Analysis and Machine Intelligence},
author = {Robins, V and Wood, P J and Sheppard, A P},
urldate = {2017-11-03},
date = {2011-08},
file = {robins2011.pdf:/home/dimitri/Zotero/storage/D4PMIRGY/robins2011.pdf:application/pdf}
}
@article{rieck_persistent_2015,
title = {Persistent Homology for the Evaluation of Dimensionality Reduction Schemes},
volume = {34},
issn = {01677055},
url = {http://doi.wiley.com/10.1111/cgf.12655},
doi = {10.1111/cgf.12655},
pages = {431--440},
number = {3},
journaltitle = {Computer Graphics Forum},
author = {Rieck, B. and Leitte, H.},
urldate = {2017-11-03},
date = {2015-06},
langid = {english},
file = {rieck2015.pdf:/home/dimitri/Zotero/storage/4VEXZ4DG/rieck2015.pdf:application/pdf}
}
@inproceedings{reininghaus_stable_2015,
title = {A stable multi-scale kernel for topological machine learning},
pages = {4741--4748},
booktitle = {Proceedings of the {IEEE} conference on computer vision and pattern recognition},
author = {Reininghaus, Jan and Huber, Stefan and Bauer, Ulrich and Kwitt, Roland},
date = {2015},
file = {reininghaus2015.pdf:/home/dimitri/Zotero/storage/H6VIHWWS/reininghaus2015.pdf:application/pdf}
}
@book{harvey_understanding_2012,
title = {Understanding high-dimensional data using Reeb graphs},
publisher = {The Ohio State University},
author = {Harvey, William John},
date = {2012},
file = {osu1342614959.pdf:/home/dimitri/Zotero/storage/M4SPU65W/osu1342614959.pdf:application/pdf}
}
@inproceedings{li_persistence-based_2014,
title = {Persistence-Based Structural Recognition},
isbn = {978-1-4799-5118-5},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6909654},
doi = {10.1109/CVPR.2014.257},
pages = {2003--2010},
publisher = {{IEEE}},
author = {Li, Chunyuan and Ovsjanikov, Maks and Chazal, Frederic},
urldate = {2017-11-03},
date = {2014-06},
file = {li2014.pdf:/home/dimitri/Zotero/storage/9JSHF2C4/li2014.pdf:application/pdf}
}
@article{krim_discovering_2016,
title = {Discovering the Whole by the Coarse: A topological paradigm for data analysis},
volume = {33},
issn = {1053-5888},
url = {http://ieeexplore.ieee.org/document/7426571/},
doi = {10.1109/MSP.2015.2510703},
shorttitle = {Discovering the Whole by the Coarse},
pages = {95--104},
number = {2},
journaltitle = {{IEEE} Signal Processing Magazine},
author = {Krim, Hamid and Gentimis, Thanos and Chintakunta, Harish},
urldate = {2017-11-03},
date = {2016-03},
file = {krim2016.pdf:/home/dimitri/Zotero/storage/379FA7KH/krim2016.pdf:application/pdf}
}
@collection{pascucci_topological_2011,
location = {Berlin, Heidelberg},
title = {Topological Methods in Data Analysis and Visualization},
isbn = {978-3-642-15013-5 978-3-642-15014-2},
url = {http://link.springer.com/10.1007/978-3-642-15014-2},
series = {Mathematics and Visualization},
publisher = {Springer Berlin Heidelberg},
editor = {Pascucci, Valerio and Tricoche, Xavier and Hagen, Hans and Tierny, Julien},
urldate = {2017-11-03},
date = {2011},
doi = {10.1007/978-3-642-15014-2},
file = {(Mathematics and Visualization) Kirk E. Jordan, Lance E. Miller (auth.), Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny (eds.)-Topological Methods in Data Analysis and Visualization_ The.pdf:/home/dimitri/Zotero/storage/IMYEDN4S/(Mathematics and Visualization) Kirk E. Jordan, Lance E. Miller (auth.), Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny (eds.)-Topological Methods in Data Analysis and Visualization_ The.pdf:application/pdf}
}
@book{edelsbrunner_computational_2010,
location = {Providence, R.I},
title = {Computational topology: an introduction},
isbn = {978-0-8218-4925-5},
shorttitle = {Computational topology},
pagetotal = {241},
publisher = {American Mathematical Society},
author = {Edelsbrunner, Herbert and Harer, J.},
date = {2010},
note = {{OCLC}: ocn427757156},
keywords = {Algorithms, Computational complexity, Data processing, Geometry, Topology},
file = {Herbert Edelsbrunner, John L. Harer-Computational Topology_ An Introduction-American Mathematical Society (2009).pdf:/home/dimitri/Zotero/storage/FWGR5NJ3/Herbert Edelsbrunner, John L. Harer-Computational Topology_ An Introduction-American Mathematical Society (2009).pdf:application/pdf}
}
@article{monasse_fast_2000,
title = {Fast computation of a contrast-invariant image representation},
volume = {9},
issn = {10577149},
url = {http://ieeexplore.ieee.org/document/841532/},
doi = {10.1109/83.841532},
pages = {860--872},
number = {5},
journaltitle = {{IEEE} Transactions on Image Processing},
author = {Monasse, P. and Guichard, F.},
urldate = {2017-11-03},
date = {2000-05},
file = {monasse2000.pdf:/home/dimitri/Zotero/storage/3UDY8L47/monasse2000.pdf:application/pdf}
}
@article{stolz_persistent_2017,
title = {Persistent homology of time-dependent functional networks constructed from coupled time series},
volume = {27},
issn = {1054-1500},
url = {http://aip.scitation.org/doi/full/10.1063/1.4978997},
doi = {10.1063/1.4978997},
abstract = {We use topological data analysis to study “functional networks” that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results. Our first example uses time-series output from networks of coupled Kuramoto oscillators. Our second example consists of biological data in the form of functional magnetic resonance imaging data that were acquired from human subjects during a simple motor-learning task in which subjects were monitored for three days during a five-day period. With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can sometimes play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used to distinguish between signal and noise. We find that persistent homology can detect differences in synchronization patterns in our data sets over time, giving insight both on changes in community structure in the networks and on increased synchronization between brain regions that form loops in a functional network during motor learning. For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops take place on the second of the three days of the learning process.},
pages = {047410},
number = {4},
journaltitle = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
shortjournal = {Chaos},
author = {Stolz, Bernadette J. and Harrington, Heather A. and Porter, Mason A.},
urldate = {2018-01-18},
date = {2017-04-01},
file = {Full Text PDF:/home/dimitri/Zotero/storage/A2BD6EHP/Stolz et al. - 2017 - Persistent homology of time-dependent functional n.pdf:application/pdf;sichaostimeseries-april2017-corrected-v4-4.pdf:/home/dimitri/Zotero/storage/2W4IQ5TQ/sichaostimeseries-april2017-corrected-v4-4.pdf:application/pdf}
}
@article{taylor_topological_2015,
title = {Topological data analysis of contagion maps for examining spreading processes on networks},
volume = {6},
issn = {2041-1723},
url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4566922/},
doi = {10.1038/ncomms8723},
abstract = {Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth’s surface; however, in modern contagions long-range edges—for example, due to airline transportation or communication media—allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct “contagion maps” that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.},
pages = {7723},
journaltitle = {Nature communications},
shortjournal = {Nat Commun},
author = {Taylor, Dane and Klimm, Florian and Harrington, Heather A. and Kramár, Miroslav and Mischaikow, Konstantin and Porter, Mason A. and Mucha, Peter J.},
urldate = {2018-01-18},
date = {2015-07-21},
pmid = {26194875},
pmcid = {PMC4566922},
file = {PubMed Central Full Text PDF:/home/dimitri/Zotero/storage/BRA55ZPK/Taylor et al. - 2015 - Topological data analysis of contagion maps for ex.pdf:application/pdf}
}
@article{stolz_topological_2016,
title = {The Topological "Shape" of Brexit},
url = {http://arxiv.org/abs/1610.00752},
abstract = {Persistent homology is a method from computational algebraic topology that can be used to study the "shape" of data. We illustrate two filtrations --- the weight rank clique filtration and the Vietoris--Rips ({VR}) filtration --- that are commonly used in persistent homology, and we apply these filtrations to a pair of data sets that are both related to the 2016 European Union "Brexit" referendum in the United Kingdom. These examples consider a topical situation and give useful illustrations of the strengths and weaknesses of these methods.},
journaltitle = {{arXiv}:1610.00752 [physics]},
author = {Stolz, Bernadette J. and Harrington, Heather A. and Porter, Mason A.},
urldate = {2018-01-18},
date = {2016-09-15},
eprinttype = {arxiv},
eprint = {1610.00752},
keywords = {Computer Science - Computational Geometry, Mathematics - Algebraic Topology, Physics - Physics and Society},
file = {arXiv\:1610.00752 PDF:/home/dimitri/Zotero/storage/9MIPK9ZY/Stolz et al. - 2016 - The Topological Shape of Brexit.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/EGR5HLE4/1610.html:text/html}
}
@article{schaub_graph_2016,
title = {Graph partitions and cluster synchronization in networks of oscillators},
volume = {26},
issn = {1054-1500},
url = {http://aip.scitation.org/doi/full/10.1063/1.4961065},
doi = {10.1063/1.4961065},
abstract = {Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators.},
pages = {094821},
number = {9},
journaltitle = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
shortjournal = {Chaos},
author = {Schaub, Michael T. and O'Clery, Neave and Billeh, Yazan N. and Delvenne, Jean-Charles and Lambiotte, Renaud and Barahona, Mauricio},
urldate = {2018-02-13},
date = {2016-08-19},
file = {Full Text PDF:/home/dimitri/Zotero/storage/QDQY8L8M/Schaub et al. - 2016 - Graph partitions and cluster synchronization in ne.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/JP2SXD5G/1.html:text/html}
}
@article{noulas_mining_2015,
title = {Mining open datasets for transparency in taxi transport in metropolitan environments},
volume = {4},
rights = {2015 Noulas et al.},
issn = {2193-1127},
url = {https://epjdatascience.springeropen.com/articles/10.1140/epjds/s13688-015-0060-2},
doi = {10.1140/epjds/s13688-015-0060-2},
abstract = {Uber has recently been introducing novel practices in urban taxi transport. Journey prices can change dynamically in almost real time and also vary geographically from one area to another in a city, a strategy known as surge pricing. In this paper, we explore the power of the new generation of open datasets towards understanding the impact of the new disruption technologies that emerge in the area of public transport. With our primary goal being a more transparent economic landscape for urban commuters, we provide a direct price comparison between Uber and the Yellow Cab company in New York. We discover that Uber, despite its lower standard pricing rates, effectively charges higher fares on average, especially during short in length, but frequent in occurrence, taxi journeys. Building on this insight, we develop a smartphone application, {OpenStreetCab}, that offers a personalized consultation to mobile users on which taxi provider is cheaper for their journey. Almost five months after its launch, the app has attracted more than three thousand users in a single city. Their journey queries have provided additional insights on the potential savings similar technologies can have for urban commuters, with a highlight being that on average, a user in New York saves 6 U.S. Dollars per taxi journey if they pick the cheapest taxi provider. We run extensive experiments to show how Uber’s surge pricing is the driving factor of higher journey prices and therefore higher potential savings for our application’s users. Finally, motivated by the observation that Uber’s surge pricing is occurring more frequently that intuitively expected, we formulate a prediction task where the aim becomes to predict a geographic area’s tendency to surge. Using exogenous to Uber data, in particular Yellow Cab and Foursquare data, we show how it is possible to estimate customer demand within an area, and by extension surge pricing, with high accuracy.},
pages = {23},
number = {1},
journaltitle = {{EPJ} Data Science},
author = {Noulas, Anastasios and Salnikov, Vsevolod and Lambiotte, Renaud and Mascolo, Cecilia},
urldate = {2018-02-13},
date = {2015-12},
file = {Full Text PDF:/home/dimitri/Zotero/storage/N6P7THVK/Noulas et al. - 2015 - Mining open datasets for transparency in taxi tran.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/H3R7HWMH/s13688-015-0060-2.html:text/html}
}
@article{tierny_topology_2017,
title = {The Topology {ToolKit}},
url = {https://hal.archives-ouvertes.fr/hal-01499905/document},
abstract = {This system paper presents the Topology {ToolKit} ({TTK}), a software platform designed for topological data analysis in scientific visualization. While topological data analysis has gained in popularity over the last two decades, it has not yet been widely adopted as a standard data analysis tool for end users or developers. {TTK} aims at addressing this problem by providing a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. {TTK} is easily accessible to end users due to a tight integration with {ParaView}. It is also easily accessible to developers through a variety of bindings (Python, {VTK}/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing {TTK}, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by {TTK}, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to {TTK} features, while still allowing for researchers powerful and easy bindings and extensions. {TTK} is open source ({BSD} license) and its code, online documentation and video tutorials are available on {TTK}'s website (https://topology-tool-kit.github.io/).},
journaltitle = {{IEEE} Transactions on Visualization and Computer Graphics},
author = {Tierny, Julien and Favelier, Guillaume and Levine, Joshua and Gueunet, Charles and Michaux, Michael},
urldate = {2018-02-15},
date = {2017-10-01},
langid = {english},
file = {Full Text PDF:/home/dimitri/Zotero/storage/TGURBQBF/Tierny et al. - 2017 - The Topology ToolKit.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/JAIQUA5K/hal-01499905v2.html:text/html}
}
@inproceedings{maria_gudhi_2014,
title = {The Gudhi Library: Simplicial Complexes and Persistent Homology},
isbn = {978-3-662-44198-5},
url = {https://link.springer.com/chapter/10.1007/978-3-662-44199-2_28},
doi = {10.1007/978-3-662-44199-2_28},
series = {Lecture Notes in Computer Science},
shorttitle = {The Gudhi Library},
abstract = {We present the main algorithmic and design choices that have been made to represent complexes and compute persistent homology in the Gudhi library. The Gudhi library (Geometric Understanding in Higher Dimensions) is a generic C++ library for computational topology. Its goal is to provide robust, efficient, flexible and easy to use implementations of state-of-the-art algorithms and data structures for computational topology. We present the different components of the software, their interaction and the user interface. We justify the algorithmic and design decisions made in Gudhi and provide benchmarks for the code. The software, which has been developped by the first author, will be available soon at project.inria.fr/gudhi/software/ .},
eventtitle = {International Congress on Mathematical Software},
pages = {167--174},
booktitle = {Mathematical Software – {ICMS} 2014},
publisher = {Springer, Berlin, Heidelberg},
author = {Maria, Clément and Boissonnat, Jean-Daniel and Glisse, Marc and Yvinec, Mariette},
urldate = {2018-02-15},
date = {2014-08-05},
langid = {english},
file = {Snapshot:/home/dimitri/Zotero/storage/3YRXLXZL/978-3-662-44199-2_28.html:text/html}
}
@online{oudot_inf556_2017,
title = {{INF}556 -- Topological Data Analysis},
url = {http://www.enseignement.polytechnique.fr/informatique/INF556/},
author = {Oudot, Steve Y.},
urldate = {2018-02-16},
date = {2017},
file = {INF556 -- Topological Data Analysis:/home/dimitri/Zotero/storage/TNRU945Q/INF556.html:text/html}
}
@article{salnikov_co-occurrence_2018,
title = {Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge},
url = {http://arxiv.org/abs/1803.04410},
shorttitle = {Co-occurrence simplicial complexes in mathematics},
abstract = {In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably losing information. In this paper we propose for the first time a simplicial complex approach to word co-occurrences, providing a natural framework for the study of higher-order relations in the space of scientific knowledge. Using topological methods we explore the conceptual landscape of mathematical research, focusing on homological holes, regions with low connectivity in the simplicial structure. We find that homological holes are ubiquitous, which suggests that they capture some essential feature of research practice in mathematics. Holes die when a subset of their concepts appear in the same article, hence their death may be a sign of the creation of new knowledge, as we show with some examples. We find a positive relation between the dimension of a hole and the time it takes to be closed: larger holes may represent potential for important advances in the field because they separate conceptually distant areas. We also show that authors' conceptual entropy is positively related with their contribution to homological holes, suggesting that polymaths tend to be on the frontier of research.},
journaltitle = {{arXiv}:1803.04410 [physics]},
author = {Salnikov, Vsevolod and Cassese, Daniele and Lambiotte, Renaud and Jones, Nick S.},
urldate = {2018-04-12},
date = {2018-03-11},
eprinttype = {arxiv},
eprint = {1803.04410},
keywords = {Physics - Physics and Society, Computer Science - Digital Libraries, Mathematics - History and Overview},
file = {arXiv\:1803.04410 PDF:/home/dimitri/Zotero/storage/HVHFGEJV/Salnikov et al. - 2018 - Co-occurrence simplicial complexes in mathematics.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/NZ7QXYNU/1803.html:text/html}
}
@article{otter_roadmap_2017,
title = {A roadmap for the computation of persistent homology},
volume = {6},
issn = {2193-1127},
url = {https://link.springer.com/article/10.1140/epjds/s13688-017-0109-5},
doi = {10.1140/epjds/s13688-017-0109-5},
abstract = {Persistent homology ({PH}) is a method used in topological data analysis ({TDA}) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. The computation of {PH} is an open area with numerous important and fascinating challenges. The field of {PH} computation is evolving rapidly, and new algorithms and software implementations are being updated and released at a rapid pace. The purposes of our article are to (1) introduce theory and computational methods for {PH} to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of {PH}. We give a friendly introduction to {PH}, navigate the pipeline for the computation of {PH} with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of {PH}. Based on our benchmarking, we indicate which algorithms and implementations are best suited to different types of data sets. In an accompanying tutorial, we provide guidelines for the computation of {PH}. We make publicly available all scripts that we wrote for the tutorial, and we make available the processed version of the data sets used in the benchmarking.},
pages = {17},
number = {1},
journaltitle = {{EPJ} Data Science},
shortjournal = {{EPJ} Data Sci.},
author = {Otter, Nina and Porter, Mason A. and Tillmann, Ulrike and Grindrod, Peter and Harrington, Heather A.},
urldate = {2018-04-12},
date = {2017-12-01},
langid = {english},
file = {Full Text PDF:/home/dimitri/Zotero/storage/UJRUWEUA/Otter et al. - 2017 - A roadmap for the computation of persistent homolo.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/6XMV77X9/s13688-017-0109-5.html:text/html}
}
@article{zomorodian_computing_2005,
title = {Computing Persistent Homology},
volume = {33},
issn = {0179-5376, 1432-0444},
url = {https://link.springer.com/article/10.1007/s00454-004-1146-y},
doi = {10.1007/s00454-004-1146-y},
abstract = {We show that the persistent homology of a filtered d-dimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analysis establishes the existence of a simple description of persistent homology groups over arbitrary fields. It also enables us to derive a natural algorithm for computing persistent homology of spaces in arbitrary dimension over any field. This result generalizes and extends the previously known algorithm that was restricted to subcomplexes of S3 and Z2 coefficients. Finally, our study implies the lack of a simple classification over non-fields. Instead, we give an algorithm for computing individual persistent homology groups over an arbitrary principal ideal domain in any dimension.},
pages = {249--274},
number = {2},
journaltitle = {Discrete \& Computational Geometry},
shortjournal = {Discrete Comput Geom},
author = {Zomorodian, Afra and Carlsson, Gunnar},
urldate = {2018-04-16},
date = {2005-02-01},
langid = {english},
file = {Full Text PDF:/home/dimitri/Zotero/storage/TB6ZGPWL/Zomorodian and Carlsson - 2005 - Computing Persistent Homology.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/HQ6KTAAF/s00454-004-1146-y.html:text/html}
}
@software{reininghaus_dipha_2018,
title = {{DIPHA} (A Distributed Persistent Homology Algorithm)},
rights = {{LGPL}-3.0},
url = {https://github.com/DIPHA/dipha},
publisher = {{DIPHA}},
author = {Reininghaus, Jan},
urldate = {2018-04-16},
date = {2018-04-03},
note = {original-date: 2015-12-25T17:23:32Z},
file = {Snapshot:/home/dimitri/Zotero/storage/VSIEADNZ/dipha.html:text/html}
}
@software{bauer_ripser:_2018,
title = {ripser: Ripser: a lean C++ code for the computation of Vietoris–Rips persistence barcodes},
rights = {{GPL}-3.0},
url = {https://github.com/Ripser/ripser},
shorttitle = {ripser},
publisher = {Ripser},
author = {Bauer, Ulrich},
urldate = {2018-04-16},
date = {2018-04-03},
note = {original-date: 2015-10-27T21:43:59Z},
file = {Snapshot:/home/dimitri/Zotero/storage/HZRP5QNK/ripser.html:text/html}
}
@book{zomorodian_topology_2009,
location = {New York, {NY}, {USA}},
title = {Topology for Computing},
isbn = {978-0-521-13609-9},
abstract = {Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, and shows how to solve real problems that have topological aspects involving computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes. Algorithms and data structures are presented when appropriate.},
publisher = {Cambridge University Press},
author = {Zomorodian, Afra J.},
date = {2009},
file = {Zomorodian - 2009 - Topology for Computing.pdf:/home/dimitri/Zotero/storage/4JNUZVQS/Zomorodian - 2009 - Topology for Computing.pdf:application/pdf}
}
@book{jonsson_simplicial_2008,
location = {Berlin},
title = {Simplicial complexes of graphs},
isbn = {978-3-540-75859-4},
url = {https://cds.cern.ch/record/1691716},
series = {Lecture Notes in Mathematics},
abstract = {A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.},
publisher = {Springer},
author = {Jonsson, Jakob},
urldate = {2018-04-16},
date = {2008},
langid = {english},
doi = {10.1007/978-3-540-75859-4, 10.1007/978-3-540-75859-4},
file = {Jonsson - 2008 - Simplicial complexes of graphs.pdf:/home/dimitri/Zotero/storage/689R2YHC/Jonsson - 2008 - Simplicial complexes of graphs.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/7CIVG53B/1691716.html:text/html}
}
@article{horak_persistent_2009,
title = {Persistent homology of complex networks},
volume = {2009},
issn = {1742-5468},
url = {http://stacks.iop.org/1742-5468/2009/i=03/a=P03034},
doi = {10.1088/1742-5468/2009/03/P03034},
abstract = {Long-lived topological features are distinguished from short-lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and presented as a parameterized version of a Betti number. Complex networks with distinct degree distributions exhibit distinct persistent topological features. Persistent topological attributes, shown to be related to the robust quality of networks, also reflect the deficiency in certain connectivity properties of networks. Random networks, networks with exponential connectivity distribution and scale-free networks were considered for homological persistency analysis.},
pages = {P03034},
number = {3},
journaltitle = {Journal of Statistical Mechanics: Theory and Experiment},
shortjournal = {J. Stat. Mech.},
author = {Horak, Danijela and Maletić, Slobodan and Rajković, Milan},
urldate = {2018-04-16},
date = {2009},
langid = {english},
file = {IOP Full Text PDF:/home/dimitri/Zotero/storage/IT5PKTTS/Horak et al. - 2009 - Persistent homology of complex networks.pdf:application/pdf}
}
@software{morozov_dionysus:_2018,
title = {dionysus: Library for computing persistent homology},
url = {https://github.com/mrzv/dionysus},
shorttitle = {dionysus},
author = {Morozov, Dimitriy},
urldate = {2018-04-16},
date = {2018-04-11},
note = {original-date: 2017-07-14T19:02:35Z},
file = {Snapshot:/home/dimitri/Zotero/storage/BBVYF9D2/dionysus.html:text/html}
}
@article{turner_frechet_2014,
title = {Fréchet Means for Distributions of Persistence Diagrams},
volume = {52},
issn = {0179-5376, 1432-0444},
url = {https://link.springer.com/article/10.1007/s00454-014-9604-7},
doi = {10.1007/s00454-014-9604-7},
abstract = {Given a distribution ρ{\textbackslash}rho on persistence diagrams and observations X1,…,Xn∼{iidρX}\_\{1\},{\textbackslash}ldots ,X\_\{n\} {\textbackslash}mathop \{{\textbackslash}sim \}{\textbackslash}limits {\textasciicircum}\{iid\} {\textbackslash}rho we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams X1,…,{XnX}\_\{1\},{\textbackslash}ldots ,X\_\{n\}. If the underlying measure ρ{\textbackslash}rho is a combination of Dirac masses ρ=1m∑mi=1{δZi}{\textbackslash}rho = {\textbackslash}frac\{1\}\{m\} {\textbackslash}sum \_\{i=1\}{\textasciicircum}\{m\} {\textbackslash}delta \_\{Z\_\{i\}\} then we prove the algorithm converges to a local minimum and a law of large numbers result for a Fréchet mean computed by the algorithm given observations drawn iid from ρ{\textbackslash}rho . We illustrate the convergence of an empirical mean computed by the algorithm to a population mean by simulations from Gaussian random fields.},
pages = {44--70},
number = {1},
journaltitle = {Discrete \& Computational Geometry},
shortjournal = {Discrete Comput Geom},
author = {Turner, Katharine and Mileyko, Yuriy and Mukherjee, Sayan and Harer, John},
urldate = {2018-04-20},
date = {2014-07-01},
langid = {english},
file = {Full Text PDF:/home/dimitri/Zotero/storage/WFNRGRL6/Turner et al. - 2014 - Fréchet Means for Distributions of Persistence Dia.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/TIA4XC3D/s00454-014-9604-7.html:text/html}
}
@article{munch_probabilistic_2015,
title = {Probabilistic Fréchet means for time varying persistence diagrams},
volume = {9},
issn = {1935-7524},
url = {https://projecteuclid.org/euclid.ejs/1433195858},
doi = {10.1214/15-EJS1030},
abstract = {Project Euclid - mathematics and statistics online},
pages = {1173--1204},
number = {1},
journaltitle = {Electronic Journal of Statistics},
author = {Munch, Elizabeth and Turner, Katharine and Bendich, Paul and Mukherjee, Sayan and Mattingly, Jonathan and Harer, John},
urldate = {2018-04-20},
date = {2015},
file = {Full Text PDF:/home/dimitri/Zotero/storage/HRY5Z3E2/Munch et al. - 2015 - Probabilistic Fréchet means for time varying persi.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/DEP25GGC/1433195858.html:text/html}
}
@article{bubenik_statistical_2015,
title = {Statistical Topological Data Analysis using Persistence Landscapes},
volume = {16},
url = {http://www.jmlr.org/papers/v16/bubenik15a.html},
pages = {77--102},
journaltitle = {Journal of Machine Learning Research},
author = {Bubenik, Peter},
urldate = {2018-04-20},
date = {2015},
file = {Full Text PDF:/home/dimitri/Zotero/storage/IQ3T72BZ/Bubenik - 2015 - Statistical Topological Data Analysis using Persis.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/94GGQHGV/bubenik15a.html:text/html}
}
@incollection{kwitt_statistical_2015,
title = {Statistical Topological Data Analysis - A Kernel Perspective},
url = {http://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective.pdf},
pages = {3070--3078},
booktitle = {Advances in Neural Information Processing Systems 28},
publisher = {Curran Associates, Inc.},
author = {Kwitt, Roland and Huber, Stefan and Niethammer, Marc and Lin, Weili and Bauer, Ulrich},
editor = {Cortes, C. and Lawrence, N. D. and Lee, D. D. and Sugiyama, M. and Garnett, R.},
urldate = {2018-04-20},
date = {2015},
file = {NIPS Full Text PDF:/home/dimitri/Zotero/storage/9NRWV859/Kwitt et al. - 2015 - Statistical Topological Data Analysis - A Kernel P.pdf:application/pdf;NIPS Snapshort:/home/dimitri/Zotero/storage/G7LF48UM/5887-statistical-topological-data-analysis-a-kernel-perspective.html:text/html}
}
@article{petri_topological_2013,
title = {Topological Strata of Weighted Complex Networks},
volume = {8},
url = {http://adsabs.harvard.edu/abs/2013PLoSO...866506P},
doi = {10.1371/journal.pone.0066506},
abstract = {The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and --more recently-- correlations between neighboring nodes. However, statistical methods quickly become
cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks. Here we introduce a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods. Their
properties divide weighted networks in two broad classes: one is characterized by small hierarchically nested holes, while the second displays larger and longer living inhomogeneities. These classes cannot be reduced to known local or quasilocal network properties, because of the intrinsic non-locality of homological properties, and thus yield a new classification built on high order coordination patterns. Our results show that topology can provide novel insights relevant for many-body interactions in social and spatial networks. Moreover, this new method creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.},
pages = {e66506},
journaltitle = {{PLoS} {ONE}},
shortjournal = {{PLoS} {ONE}},
author = {Petri, Giovanni and Scolamiero, Martina and Donato, Irene and Vaccarino, Francesco},
urldate = {2018-04-20},
date = {2013-06-01},
file = {Topological Strata of Weighted Complex Networks.PDF:/home/dimitri/Zotero/storage/X43JU3GL/Topological Strata of Weighted Complex Networks.PDF:application/pdf}
}
@inproceedings{carlsson_zigzag_2009,
location = {New York, {NY}, {USA}},
title = {Zigzag Persistent Homology and Real-valued Functions},
isbn = {978-1-60558-501-7},
url = {http://doi.acm.org/10.1145/1542362.1542408},
doi = {10.1145/1542362.1542408},
series = {{SCG} '09},
abstract = {We study the problem of computing zigzag persistence of a sequence of homology groups and study a particular sequence derived from the levelsets of a real-valued function on a topological space. The result is a local, symmetric interval descriptor of the function. Our structural results establish a connection between the zigzag pairs in this sequence and extended persistence, and in the process resolve an open question associated with the latter. Our algorithmic results not only provide a way to compute zigzag persistence for any sequence of homology groups, but combined with our structural results give a novel algorithm for computing extended persistence. This algorithm is easily parallelizable and uses (asymptotically) less memory.},
pages = {247--256},
booktitle = {Proceedings of the Twenty-fifth Annual Symposium on Computational Geometry},
publisher = {{ACM}},
author = {Carlsson, Gunnar and de Silva, Vin and Morozov, Dmitriy},
urldate = {2018-04-20},
date = {2009},
keywords = {algorithms, extended persistence, levelset zigzag, Mayer-Vietoris pyramid, zigzag persistent homology},
file = {Carlsson et al. - 2009 - Zigzag Persistent Homology and Real-valued Functio.pdf:/home/dimitri/Zotero/storage/WNIUXA7Y/Carlsson et al. - 2009 - Zigzag Persistent Homology and Real-valued Functio.pdf:application/pdf}
}
@inproceedings{dey_computing_2014,
location = {New York, {NY}, {USA}},
title = {Computing Topological Persistence for Simplicial Maps},
isbn = {978-1-4503-2594-3},
url = {http://doi.acm.org/10.1145/2582112.2582165},
doi = {10.1145/2582112.2582165},
series = {{SOCG}'14},
abstract = {Algorithms for persistent homology are well-studied where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under Z2 coefficients for a (monotone) sequence of general simplicial maps and show how these maps arise naturally in some applications of topological data analysis. A simplicial map can be decomposed into a set of elementary inclusions and vertex collapses--two atomic operations that can be supported efficiently with the notion of simplex annotations for computing persistent homology. A consistent annotation through these atomic operations implies the maintenance of a consistent cohomology basis, hence a homology basis by duality. While the idea of maintaining a cohomology basis through an inclusion is not new, maintaining them through a vertex collapse is new, which constitutes an important atomic operation for simulating simplicial maps. Annotations support the vertex collapse in addition to the usual inclusion quite naturally. Finally, we exhibit an application of this new tool in which we approximate the persistence diagram of a filtration of Rips complexes where vertex collapses are used to tame the blow-up in size.},
pages = {345:345--345:354},
booktitle = {Proceedings of the Thirtieth Annual Symposium on Computational Geometry},
publisher = {{ACM}},
author = {Dey, Tamal K. and Fan, Fengtao and Wang, Yusu},
urldate = {2018-04-20},
date = {2014},
keywords = {cohomology, homology, simplicial maps, topological data analysis, Topological persistence},
file = {Dey et al. - 2014 - Computing Topological Persistence for Simplicial M.pdf:/home/dimitri/Zotero/storage/X6R4GKRU/Dey et al. - 2014 - Computing Topological Persistence for Simplicial M.pdf:application/pdf}
}
@article{carlsson_theory_2009,
title = {The Theory of Multidimensional Persistence},
volume = {42},
issn = {0179-5376, 1432-0444},
url = {https://link.springer.com/article/10.1007/s00454-009-9176-0},
doi = {10.1007/s00454-009-9176-0},
abstract = {Persistent homology captures the topology of a filtration—a one-parameter family of increasing spaces—in terms of a complete discrete invariant. This invariant is a multiset of intervals that denote the lifetimes of the topological entities within the filtration. In many applications of topology, we need to study a multifiltration: a family of spaces parameterized along multiple geometric dimensions. In this paper, we show that no similar complete discrete invariant exists for multidimensional persistence. Instead, we propose the rank invariant, a discrete invariant for the robust estimation of Betti numbers in a multifiltration, and prove its completeness in one dimension.},
pages = {71--93},
number = {1},
journaltitle = {Discrete \& Computational Geometry},
shortjournal = {Discrete Comput Geom},
author = {Carlsson, Gunnar and Zomorodian, Afra},
urldate = {2018-04-30},
date = {2009-07-01},
langid = {english},
file = {10.1.1.86.1620.pdf:/home/dimitri/Zotero/storage/4EEYB2MK/10.1.1.86.1620.pdf:application/pdf;Full Text PDF:/home/dimitri/Zotero/storage/RBN5LKT6/Carlsson and Zomorodian - 2009 - The Theory of Multidimensional Persistence.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/PT7Q4KVU/10.html:text/html}
}
@article{perea_sliding_2017,
title = {Sliding windows and persistence},
volume = {141},
issn = {0001-4966},
url = {https://asa.scitation.org/doi/abs/10.1121/1.4987655},
doi = {10.1121/1.4987655},
pages = {3585--3585},
number = {5},
journaltitle = {The Journal of the Acoustical Society of America},
shortjournal = {The Journal of the Acoustical Society of America},
author = {Perea, Jose and Traile, Chris},
urldate = {2018-05-02},
date = {2017-05-01},
file = {Snapshot:/home/dimitri/Zotero/storage/NAPFXSEL/1.html:text/html}
}
@article{perea_sliding_2015,
title = {Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis},
volume = {15},
issn = {1615-3375, 1615-3383},
url = {https://link.springer.com/article/10.1007/s10208-014-9206-z},
doi = {10.1007/s10208-014-9206-z},
shorttitle = {Sliding Windows and Persistence},
abstract = {We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window embeddings, as seen through the lens of persistent homology. In particular, we show that maximum persistence at the point-cloud level can be used to quantify periodicity at the signal level, prove structural and convergence theorems for the resulting persistence diagrams, and derive estimates for their dependency on window size and embedding dimension. We apply this methodology to quantifying periodicity in synthetic data sets and compare the results with those obtained using state-of-the-art methods in gene expression analysis. We call this new method {SW}1PerS, which stands for Sliding Windows and 1-Dimensional Persistence Scoring.},
pages = {799--838},
number = {3},
journaltitle = {Foundations of Computational Mathematics},
shortjournal = {Found Comput Math},
author = {Perea, Jose A. and Harer, John},
urldate = {2018-05-02},
date = {2015-06-01},
langid = {english},
file = {Perea and Harer - 2015 - Sliding Windows and Persistence An Application of.pdf:/home/dimitri/Zotero/storage/2PSQQ8F4/Perea and Harer - 2015 - Sliding Windows and Persistence An Application of.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/UDRR3GRW/s10208-014-9206-z.html:text/html}
}
@article{perea_sw1pers:_2015,
title = {{SW}1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data},
volume = {16},
issn = {1471-2105},
url = {https://doi.org/10.1186/s12859-015-0645-6},
doi = {10.1186/s12859-015-0645-6},
shorttitle = {{SW}1PerS},
abstract = {Identifying periodically expressed genes across different processes (e.g. the cell and metabolic cycles, circadian rhythms, etc) is a central problem in computational biology. Biological time series may contain (multiple) unknown signal shapes of systemic relevance, imperfections like noise, damping, and trending, or limited sampling density. While there exist methods for detecting periodicity, their design biases (e.g. toward a specific signal shape) can limit their applicability in one or more of these situations.},
pages = {257},
journaltitle = {{BMC} Bioinformatics},
shortjournal = {{BMC} Bioinformatics},
author = {Perea, Jose A. and Deckard, Anastasia and Haase, Steve B. and Harer, John},
urldate = {2018-05-02},
date = {2015-08-16},
keywords = {Gene expression, Periodicity, Persistent homology, Sliding windows, Time series},
file = {Full Text PDF:/home/dimitri/Zotero/storage/YH7DK289/Perea et al. - 2015 - SW1PerS Sliding windows and 1-persistence scoring.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/2N8XI4AJ/s12859-015-0645-6.html:text/html}
}
@inproceedings{seversky_time-series_2016,
title = {On Time-Series Topological Data Analysis: New Data and Opportunities},
doi = {10.1109/CVPRW.2016.131},
shorttitle = {On Time-Series Topological Data Analysis},
abstract = {This work introduces a new dataset and framework for the exploration of topological data analysis ({TDA}) techniques applied to time-series data. We examine the end-toend {TDA} processing pipeline for persistent homology applied to time-delay embeddings of time series - embeddings that capture the underlying system dynamics from which time series data is acquired. In particular, we consider stability with respect to time series length, the approximation accuracy of sparse filtration methods, and the discriminating ability of persistence diagrams as a feature for learning. We explore these properties across a wide range of time-series datasets spanning multiple domains for single source multi-segment signals as well as multi-source single segment signals. Our analysis and dataset captures the entire {TDA} processing pipeline and includes time-delay embeddings, persistence diagrams, topological distance measures, as well as kernels for similarity learning and classification tasks for a broad set of time-series data sources. We outline the {TDA} framework and rationale behind the dataset and provide insights into the role of {TDA} for time-series analysis as well as opportunities for new work.},
eventtitle = {2016 {IEEE} Conference on Computer Vision and Pattern Recognition Workshops ({CVPRW})},
pages = {1014--1022},
booktitle = {2016 {IEEE} Conference on Computer Vision and Pattern Recognition Workshops ({CVPRW})},
author = {Seversky, L. M. and Davis, S. and Berger, M.},
date = {2016-06},
keywords = {Topology, topological data analysis, approximation accuracy, approximation theory, Context, data analysis, embedded systems, Kernel, learning feature, Pipelines, signal processing, single source multisegment signals, sparse filtration methods, Support vector machines, system dynamics, {TDA}, Three-dimensional displays, time series, Time series analysis, time-delay embeddings, time-series data},
file = {IEEE Xplore Abstract Record:/home/dimitri/Zotero/storage/BINURQ6P/7789621.html:text/html;Seversky et al. - 2016 - On Time-Series Topological Data Analysis New Data.pdf:/home/dimitri/Zotero/storage/7BBZHTTF/Seversky et al. - 2016 - On Time-Series Topological Data Analysis New Data.pdf:application/pdf}
}
@article{cang_evolutionary_2018,
title = {Evolutionary homology on coupled dynamical systems},
url = {http://arxiv.org/abs/1802.04677},
abstract = {Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze the topological persistence over spatial scales, persistent homology has rarely been devised for time evolution. We propose the use of a new filtration function for persistent homology which takes as input the adjacent oscillator trajectories of a dynamical system. We also regulate the dynamical system by a weighted graph Laplacian matrix derived from the network of interest, which embeds the topological connectivity of the network into the dynamical system. The resulting topological signatures, which we call evolutionary homology ({EH}) barcodes, reveal the topology-function relationship of the network and thus give rise to the quantitative analysis of nodal properties. The proposed {EH} is applied to protein residue networks for protein thermal fluctuation analysis, rendering the most accurate B-factor prediction of a set of 364 proteins. This work extends the utility of dynamical systems to the quantitative modeling and analysis of realistic physical systems.},
journaltitle = {{arXiv}:1802.04677 [math, q-bio]},
author = {Cang, Zixuan and Munch, Elizabeth and Wei, Guo-Wei},
urldate = {2018-05-02},
date = {2018-02-13},
eprinttype = {arxiv},
eprint = {1802.04677},
keywords = {Mathematics - Algebraic Topology, Mathematics - Dynamical Systems, Quantitative Biology - Quantitative Methods},
file = {arXiv\:1802.04677 PDF:/home/dimitri/Zotero/storage/6RNFZZ93/Cang et al. - 2018 - Evolutionary homology on coupled dynamical systems.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/984CQS7D/1802.html:text/html}
}
@article{umeda_time_2017,
title = {Time Series Classification via Topological Data Analysis},
volume = {32},
issn = {1346-0714},
url = {http://adsabs.harvard.edu/abs/2017TJSAI..32G..72U},
doi = {10.1527/tjsai.D-G72},
abstract = {Not Available},
journaltitle = {Transactions of the Japanese Society for Artificial Intelligence},
shortjournal = {Transactions of the Japanese Society for Artificial Intelligence},
author = {Umeda, Yuhei},
urldate = {2018-05-02},
date = {2017},
file = {Umeda - 2017 - Time Series Classification via Topological Data An.pdf:/home/dimitri/Zotero/storage/YK5UQZ4D/Umeda - 2017 - Time Series Classification via Topological Data An.pdf:application/pdf}
}
@article{kusano_kernel_2017,
title = {Kernel method for persistence diagrams via kernel embedding and weight factor},
url = {http://arxiv.org/abs/1706.03472},
abstract = {Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy topological properties. Nowadays, it is highly desired to develop a statistical framework on persistence diagrams to deal with practical data. This paper proposes a kernel method on persistence diagrams. A theoretical contribution of our method is that the proposed kernel allows one to control the effect of persistence, and, if necessary, noisy topological properties can be discounted in data analysis. Furthermore, the method provides a fast approximation technique. The method is applied into several problems including practical data in physics, and the results show the advantage compared to the existing kernel method on persistence diagrams.},
journaltitle = {{arXiv}:1706.03472 [physics, stat]},
author = {Kusano, Genki and Fukumizu, Kenji and Hiraoka, Yasuaki},
urldate = {2018-06-12},
date = {2017-06-12},
eprinttype = {arxiv},
eprint = {1706.03472},
keywords = {Statistics - Machine Learning, Mathematics - Algebraic Topology, Physics - Data Analysis, Statistics and Probability},
file = {arXiv\:1706.03472 PDF:/home/dimitri/Zotero/storage/ISLEIEE9/Kusano et al. - 2017 - Kernel method for persistence diagrams via kernel .pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/6FIXWZVF/1706.html:text/html}
}
@article{adams_persistence_2017,
title = {Persistence Images: A Stable Vector Representation of Persistent Homology},
volume = {18},
url = {http://jmlr.org/papers/v18/16-337.html},
shorttitle = {Persistence Images},
abstract = {Many data sets can be viewed as a noisy sampling of an
underlying space, and tools from topological data analysis can
characterize this structure for the purpose of knowledge
discovery. One such tool is persistent homology, which provides
a multiscale description of the homological features within a
data set. A useful representation of this homological
information is a persistence diagram ({PD}). Efforts have
been made to map {PDs} into spaces with additional structure
valuable to machine learning tasks. We convert a {PD} to a finite-
dimensional vector representation which we call a
persistence image ({PI}), and prove the stability of this
transformation with respect to small perturbations in the
inputs. The discriminatory power of {PIs} is compared against
existing methods, showing significant performance gains. We
explore the use of {PIs} with vector-based machine learning tools,
such as linear sparse support vector machines, which identify
features containing discriminating topological information.
Finally, high accuracy inference of parameter values from the
dynamic output of a discrete dynamical system (the linked
twist map) and a partial differential equation (the
anisotropic Kuramoto-Sivashinsky equation) provide a
novel application of the discriminatory power of {PIs}.},
pages = {1--35},
number = {8},
journaltitle = {Journal of Machine Learning Research},
author = {Adams, Henry and Emerson, Tegan and Kirby, Michael and Neville, Rachel and Peterson, Chris and Shipman, Patrick and Chepushtanova, Sofya and Hanson, Eric and Motta, Francis and Ziegelmeier, Lori},
urldate = {2018-06-12},
date = {2017},
file = {Fulltext PDF:/home/dimitri/Zotero/storage/EUWNMLQF/Adams et al. - 2017 - Persistence Images A Stable Vector Representation.pdf:application/pdf}
}
@article{bubenik_statistical_2015-1,
title = {Statistical Topological Data Analysis using Persistence Landscapes},
volume = {16},
url = {http://www.jmlr.org/papers/v16/bubenik15a.html},
pages = {77--102},
journaltitle = {Journal of Machine Learning Research},
author = {Bubenik, Peter},
urldate = {2018-06-12},
date = {2015},
file = {Full Text PDF:/home/dimitri/Zotero/storage/CJW9F5XG/Bubenik - 2015 - Statistical Topological Data Analysis using Persis.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/E2DN26NP/bubenik15a.html:text/html}
}
@article{kalisnik_tropical_2018,
title = {Tropical Coordinates on the Space of Persistence Barcodes},
issn = {1615-3375, 1615-3383},
url = {https://link.springer.com/article/10.1007/s10208-018-9379-y},
doi = {10.1007/s10208-018-9379-y},
abstract = {The aim of applied topology is to use and develop topological methods for applied mathematics, science and engineering. One of the main tools is persistent homology, an adaptation of classical homology, which assigns a barcode, i.e., a collection of intervals, to a finite metric space. Because of the nature of the invariant, barcodes are not well adapted for use by practitioners in machine learning tasks. We can circumvent this problem by assigning numerical quantities to barcodes, and these outputs can then be used as input to standard algorithms. It is the purpose of this paper to identify tropical coordinates on the space of barcodes and prove that they are stable with respect to the bottleneck distance and Wasserstein distances.},
pages = {1--29},
journaltitle = {Foundations of Computational Mathematics},
shortjournal = {Found Comput Math},
author = {Kališnik, Sara},
urldate = {2018-06-13},
date = {2018-01-30},
langid = {english},
file = {Full Text PDF:/home/dimitri/Zotero/storage/VIP5PCKK/Kališnik - 2018 - Tropical Coordinates on the Space of Persistence B.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/U2VKTXMW/10.html:text/html}
}
@article{le_persistence_2018,
title = {Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams},
url = {http://arxiv.org/abs/1802.03569},
shorttitle = {Persistence Fisher Kernel},
abstract = {Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, {\textbackslash}textit\{persistent homology\} is a well-known tool to extract robust topological features, and outputs as {\textbackslash}textit\{persistence diagrams\} ({PDs}). However, {PDs} are point multi-sets which can not be used in machine learning algorithms for vector data. To deal with it, an emerged approach is to use kernel methods, and an appropriate geometry for {PDs} is an important factor to measure the similarity of {PDs}. A popular geometry for {PDs} is the {\textbackslash}textit\{Wasserstein metric\}. However, Wasserstein distance is not {\textbackslash}textit\{negative definite\}. Thus, it is limited to build positive definite kernels upon the Wasserstein distance {\textbackslash}textit\{without approximation\}. In this work, we rely upon the alternative {\textbackslash}textit\{Fisher information geometry\} to propose a positive definite kernel for {PDs} {\textbackslash}textit\{without approximation\}, namely the Persistence Fisher ({PF}) kernel. Then, we analyze eigensystem of the integral operator induced by the proposed kernel for kernel machines. Based on that, we derive generalization error bounds via covering numbers and Rademacher averages for kernel machines with the {PF} kernel. Additionally, we show some nice properties such as stability and infinite divisibility for the proposed kernel. Furthermore, we also propose a linear time complexity over the number of points in {PDs} for an approximation of our proposed kernel with a bounded error. Throughout experiments with many different tasks on various benchmark datasets, we illustrate that the {PF} kernel compares favorably with other baseline kernels for {PDs}.},
journaltitle = {{arXiv}:1802.03569 [cs, math, stat]},
author = {Le, Tam and Yamada, Makoto},
urldate = {2018-06-18},
date = {2018-02-10},
eprinttype = {arxiv},
eprint = {1802.03569},
keywords = {Computer Science - Learning, Statistics - Machine Learning, Mathematics - Algebraic Topology},
file = {arXiv\:1802.03569 PDF:/home/dimitri/Zotero/storage/RYBJTQ9F/Le and Yamada - 2018 - Persistence Fisher Kernel A Riemannian Manifold K.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/4P6MP6RX/1802.html:text/html}
}
@inproceedings{reininghaus_stable_2015-1,
title = {A stable multi-scale kernel for topological machine learning},
doi = {10.1109/CVPR.2015.7299106},
abstract = {Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel {SVMs} or kernel {PCA}. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes.},
eventtitle = {2015 {IEEE} Conference on Computer Vision and Pattern Recognition ({CVPR})},
pages = {4741--4748},
booktitle = {2015 {IEEE} Conference on Computer Vision and Pattern Recognition ({CVPR})},
author = {Reininghaus, J. and Huber, S. and Bauer, U. and Kwitt, R.},
date = {2015-06},
keywords = {1-Wasserstein distance, 3D shape classification, 3D shape retrieval, image classification, image retrieval, image texture, learning (artificial intelligence), multiscale kernel, persistence diagrams, shape recognition, texture recognition, topological machine learning, Yttrium},
file = {IEEE Xplore Abstract Record:/home/dimitri/Zotero/storage/R29X3VFL/7299106.html:text/html;Reininghaus et al. - 2015 - A stable multi-scale kernel for topological machin.pdf:/home/dimitri/Zotero/storage/K3FZI79D/Reininghaus et al. - 2015 - A stable multi-scale kernel for topological machin.pdf:application/pdf}
}
@inproceedings{carriere_sliced_2017,
title = {Sliced Wasserstein Kernel for Persistence Diagrams},
url = {http://proceedings.mlr.press/v70/carriere17a.html},
abstract = {Persistence diagrams ({PDs}) play a key role in topological data analysis ({TDA}), in which they are routinely used to describe succinctly complex topological properties of complicated shapes. {PDs} enjo...},
eventtitle = {International Conference on Machine Learning},
pages = {664--673},
booktitle = {International Conference on Machine Learning},
author = {Carrière, Mathieu and Cuturi, Marco and Oudot, Steve},
urldate = {2018-06-20},
date = {2017-07-17},
langid = {english},
file = {arXiv\:1706.03358 PDF:/home/dimitri/Zotero/storage/NWMEA95P/Carrière et al. - 2017 - Sliced Wasserstein Kernel for Persistence Diagrams.pdf:application/pdf;Full Text PDF:/home/dimitri/Zotero/storage/7FZZJDKP/Carrière et al. - 2017 - Sliced Wasserstein Kernel for Persistence Diagrams.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/VDXI2J8D/carriere17a.html:text/html}
}

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@ -265,9 +265,10 @@ once: this is the objective of \emph{filtered simplical complexes}.
\label{sec:persistent-homology}
We can now compute the homology for each step in a filtration. This
leads to the notion of \emph{persistent homology}, which gives us all
the information necessary to establish the topological structure of
the metric space at multiple scales.
leads to the notion of \emph{persistent
homology}~\cite{carlsson_topology_2009,zomorodian_computing_2005},
which gives us all the information necessary to establish the
topological structure of the metric space at multiple scales.
\begin{defn}[Persistent homology]
The \emph{$p$-th persistent homology} of a simplicial complex
@ -378,11 +379,12 @@ build simplicial complexes on graphs.
\end{defn}
Temporal networks are defined in the more general framework of
\emph{multilayer networks}. However, this definition is much too
general for our simple applications, and we restrict ourselves to
edge-centric time-varying graphs. In this model, the set of nodes is
fixed and doesn't change over time, whereas edges can appear or
disappear at different timestamps.
\emph{multilayer networks}~\cite{kivela_multilayer_2014}. However,
this definition is much too general for our simple applications, and
we restrict ourselves to edge-centric time-varying
graphs~\cite{casteigts_time-varying_2012}. In this model, the set of
nodes is fixed and doesn't change over time, whereas edges can appear
or disappear at different timestamps.
\begin{defn}[Temporal network]
A \emph{temporal network} (or graph) is a tuple
@ -470,14 +472,15 @@ data. An undirected network is already a simplicial complex of
dimension 1. However, this will not be sufficient to capture enough
topological information: we need to introduce higher-dimensional
simplices. The first possible method is to project the network on a
metric space, thus transforming the network data into a point cloud
data. For this, we need to compute the distance between each pair of
nodes in the network (via shortest path distance for instance). This
also requires the network to be connected.
metric space~\cite{otter_roadmap_2017}, thus transforming the network
data into a point cloud data. For this, we need to compute the
distance between each pair of nodes in the network (via shortest path
distance for instance). This also requires the network to be
connected.
Another usual method for weighted networks is called the \emph{weight
rank clique filtration} (WRCF), which filters the network based on
weights. The procedure works as follows:
rank clique filtration} (WRCF)~\cite{petri_topological_2013}, which
filters the network based on weights. The procedure works as follows:
\begin{enumerate}
\item Set the set of all nodes, without any edge, as filtration
step~0.

5
dissertation/preamble.tex
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@ -7,8 +7,6 @@
\usepackage{polyglossia}
\setdefaultlanguage[variant=british]{english}
\usepackage{lipsum}
\usepackage{graphicx}
\usepackage[dvipsnames]{xcolor}
\usepackage{wrapfig}
@ -35,6 +33,9 @@
\usepackage{tikz}
\usetikzlibrary{patterns,backgrounds,positioning}
\usepackage{biblatex}
\bibliography{TDA,temporalgraphs}
\usepackage{pdfpages}
\usepackage{microtype}

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@ -0,0 +1,389 @@
@article{tabourier_predicting_2016,
title = {Predicting links in ego-networks using temporal information},
volume = {5},
rights = {2016 Tabourier et al.},
issn = {2193-1127},
url = {https://epjdatascience.springeropen.com/articles/10.1140/epjds/s13688-015-0062-0},
doi = {10.1140/epjds/s13688-015-0062-0},
abstract = {Link prediction appears as a central problem of network science, as it calls for unfolding the mechanisms that govern the micro-dynamics of the network. In this work, we are interested in ego-networks, that is the mere information of interactions of a node to its neighbors, in the context of social relationships. As the structural information is very poor, we rely on another source of information to predict links among egos’ neighbors: the timing of interactions. We define several features to capture different kinds of temporal information and apply machine learning methods to combine these various features and improve the quality of the prediction. We demonstrate the efficiency of this temporal approach on a cellphone interaction dataset, pointing out features which prove themselves to perform well in this context, in particular the temporal profile of interactions and elapsed time between contacts.},
pages = {1},
number = {1},
journaltitle = {{EPJ} Data Science},
author = {Tabourier, Lionel and Libert, Anne-Sophie and Lambiotte, Renaud},
urldate = {2018-02-13},
date = {2016-12},
file = {Full Text PDF:/home/dimitri/Zotero/storage/ETM66HPY/Tabourier et al. - 2016 - Predicting links in ego-networks using temporal in.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/IUNKJ9YF/s13688-015-0062-0.html:text/html}
}
@article{kivela_multilayer_2014,
title = {Multilayer Networks},
volume = {2},
issn = {2051-1310, 2051-1329},
url = {http://arxiv.org/abs/1309.7233},
doi = {10.1093/comnet/cnu016},
abstract = {In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.},
pages = {203--271},
number = {3},
journaltitle = {Journal of Complex Networks},
author = {Kivelä, Mikko and Arenas, Alexandre and Barthelemy, Marc and Gleeson, James P. and Moreno, Yamir and Porter, Mason A.},
urldate = {2018-02-13},
date = {2014-09-01},
eprinttype = {arxiv},
eprint = {1309.7233},
keywords = {Physics - Physics and Society, Computer Science - Social and Information Networks},
file = {arXiv\:1309.7233 PDF:/home/dimitri/Zotero/storage/F98JFB2E/Kivelä et al. - 2014 - Multilayer Networks.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/7WBJRIBQ/1309.html:text/html}
}
@article{porter_dynamical_2014,
title = {Dynamical Systems on Networks: A Tutorial},
url = {http://arxiv.org/abs/1403.7663},
shorttitle = {Dynamical Systems on Networks},
abstract = {We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.},
journaltitle = {{arXiv}:1403.7663 [cond-mat, physics:nlin, physics:physics]},
author = {Porter, Mason A. and Gleeson, James P.},
urldate = {2018-02-13},
date = {2014-03-29},
eprinttype = {arxiv},
eprint = {1403.7663},
keywords = {Physics - Physics and Society, Computer Science - Social and Information Networks, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Nonlinear Sciences - Adaptation and Self-Organizing Systems},
file = {arXiv\:1403.7663 PDF:/home/dimitri/Zotero/storage/XBRAHARB/Porter and Gleeson - 2014 - Dynamical Systems on Networks A Tutorial.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/LF7GCTFE/1403.html:text/html}
}
@article{casteigts_time-varying_2012,
title = {Time-varying graphs and dynamic networks},
volume = {27},
issn = {1744-5760},
url = {https://doi.org/10.1080/17445760.2012.668546},
doi = {10.1080/17445760.2012.668546},
abstract = {The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems – delay-tolerant networks, opportunistic-mobility networks and social networks – obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe, and the formal models proposed so far to express some specific concepts are the components of a larger formal description of this universe. The main contribution of this paper is to integrate the vast collection of concepts, formalisms and results found in the literature into a unified framework, which we call time-varying graphs ({TVGs}). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. Based on this definitional work, employing both existing results and original observations, we present a hierarchical classification of {TVGs}; each class corresponds to a significant property examined in the distributed computing literature. We then examine how {TVGs} can be used to study the evolution of network properties, and propose different techniques, depending on whether the indicators for these properties are atemporal (as in the majority of existing studies) or temporal. Finally, we briefly discuss the introduction of randomness in {TVGs}.},
pages = {387--408},
number = {5},
journaltitle = {International Journal of Parallel, Emergent and Distributed Systems},
author = {Casteigts, Arnaud and Flocchini, Paola and Quattrociocchi, Walter and Santoro, Nicola},
urldate = {2018-02-21},
date = {2012-10-01},
keywords = {social networks, delay-tolerant networks, distributed computing, dynamic graphs, opportunistic networks, time-varying graphs},
file = {1012.0009.pdf:/home/dimitri/Zotero/storage/IPW9FMKH/1012.0009.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/R94NRJG7/17445760.2012.html:text/html}
}
@article{kuhn_dynamic_2011,
title = {Dynamic Networks: Models and Algorithms},
volume = {42},
issn = {0163-5700},
url = {http://doi.acm.org/10.1145/1959045.1959064},
doi = {10.1145/1959045.1959064},
shorttitle = {Dynamic Networks},
pages = {82--96},
number = {1},
journaltitle = {{SIGACT} News},
author = {Kuhn, Fabian and Oshman, Rotem},
urldate = {2018-02-21},
date = {2011-03},
file = {kuhn2011.pdf:/home/dimitri/Zotero/storage/WEN85Y2C/kuhn2011.pdf:application/pdf}
}
@article{michail_introduction_2016,
title = {An Introduction to Temporal Graphs: An Algorithmic Perspective},
volume = {12},
issn = {1542-7951},
url = {https://doi.org/10.1080/15427951.2016.1177801},
doi = {10.1080/15427951.2016.1177801},
shorttitle = {An Introduction to Temporal Graphs},
abstract = {A temporal graph is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed as a sequence G1, G2…, Gl of static graphs over the same (static) set of nodes V. Though static graphs have been extensively studied, for their temporal generalization we are still far from having a concrete set of structural and algorithmic principles. Recent research shows that many graph properties and problems become radically different and usually substantially more difficult when an extra time dimension is added to them. Moreover, there is already a rich and rapidly growing set of modern systems and applications that can be naturally modeled and studied via temporal graphs. This, further motivates the need for the development of a temporal extension of graph theory. We survey here recent results on temporal graphs and temporal graph problems that have appeared in the Computer Science community.},
pages = {239--280},
number = {4},
journaltitle = {Internet Mathematics},
author = {Michail, Othon},
urldate = {2018-02-21},
date = {2016-07-03},
file = {1503.00278.pdf:/home/dimitri/Zotero/storage/QQU5QN6M/1503.00278.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/A9KBYDWN/15427951.2016.html:text/html}
}
@article{kempe_connectivity_2002,
title = {Connectivity and Inference Problems for Temporal Networks},
volume = {64},
issn = {0022-0000},
url = {http://www.sciencedirect.com/science/article/pii/S0022000002918295},
doi = {10.1006/jcss.2002.1829},
abstract = {Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. In such settings, a natural model is that of a graph in which each edge is annotated with a time label specifying the time at which its endpoints “communicated.” We will call such a graph a temporal network. To model the notion that information in such a network “flows” only on paths whose labels respect the ordering of time, we call a path time-respecting if the time labels on its edges are non-decreasing. The central motivation for our work is the following question: how do the basic combinatorial and algorithmic properties of graphs change when we impose this additional temporal condition? The notion of a path is intrinsic to many of the most fundamental algorithmic problems on graphs; spanning trees, connectivity, flows, and cuts are some examples. When we focus on time-respecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the traditional setting, but very rich in its own right. We provide results on two types of problems for temporal networks. First, we consider connectivity problems, in which we seek disjoint time-respecting paths between pairs of nodes. The natural analogue of Menger's Theorem for node-disjoint paths fails in general for time-respecting paths; we give a non-trivial characterization of those graphs for which the theorem does hold in terms of an excluded subdivision theorem, and provide a polynomial-time algorithm for connectivity on this class of graphs. (The problem on general graphs is {NP}-complete.) We then define and study the class of inference problems, in which we seek to reconstruct a partially specified time labeling of a network in a manner consistent with an observed history of information flow.},
pages = {820--842},
number = {4},
journaltitle = {Journal of Computer and System Sciences},
shortjournal = {Journal of Computer and System Sciences},
author = {Kempe, David and Kleinberg, Jon and Kumar, Amit},
urldate = {2018-02-22},
date = {2002-06-01},
file = {10.1.1.30.6741.pdf:/home/dimitri/Zotero/storage/I9CR9UGA/10.1.1.30.6741.pdf:application/pdf;ScienceDirect Snapshot:/home/dimitri/Zotero/storage/87E98N2I/S0022000002918295.html:text/html}
}
@inproceedings{mertzios_temporal_2013,
title = {Temporal Network Optimization Subject to Connectivity Constraints},
isbn = {978-3-642-39211-5 978-3-642-39212-2},
url = {https://link.springer.com/chapter/10.1007/978-3-642-39212-2_57},
doi = {10.1007/978-3-642-39212-2_57},
series = {Lecture Notes in Computer Science},
abstract = {In this work we consider temporal networks, i.e. networks defined by a labeling λ assigning to each edge of an underlying graph G a set of discrete time-labels. The labels of an edge, which are natural numbers, indicate the discrete time moments at which the edge is available. We focus on path problems of temporal networks. In particular, we consider time-respecting paths, i.e. paths whose edges are assigned by λ a strictly increasing sequence of labels. We begin by giving two efficient algorithms for computing shortest time-respecting paths on a temporal network. We then prove that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks. Finally, we propose two cost minimization parameters for temporal network design. One is the temporality of G, in which the goal is to minimize the maximum number of labels of an edge, and the other is the temporal cost of G, in which the goal is to minimize the total number of labels used. Optimization of these parameters is performed subject to some connectivity constraint. We prove several lower and upper bounds for the temporality and the temporal cost of some very basic graph families such as rings, directed acyclic graphs, and trees.},
eventtitle = {International Colloquium on Automata, Languages, and Programming},
pages = {657--668},
booktitle = {Automata, Languages, and Programming},
publisher = {Springer, Berlin, Heidelberg},
author = {Mertzios, George B. and Michail, Othon and Chatzigiannakis, Ioannis and Spirakis, Paul G.},
urldate = {2018-02-22},
date = {2013-07-08},
langid = {english},
file = {1502.04382.pdf:/home/dimitri/Zotero/storage/AUZGZX8M/1502.04382.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/8AUNJDZ2/978-3-642-39212-2_57.html:text/html}
}
@article{akrida_ephemeral_2016,
title = {Ephemeral networks with random availability of links: The case of fast networks},
volume = {87},
issn = {0743-7315},
url = {http://www.sciencedirect.com/science/article/pii/S0743731515001872},
doi = {10.1016/j.jpdc.2015.10.002},
shorttitle = {Ephemeral networks with random availability of links},
abstract = {We consider here a model of temporal networks, the links of which are available only at certain moments in time, chosen randomly from a subset of the positive integers. We define the notion of the Temporal Diameter of such networks. We also define fast and slow such temporal networks with respect to the expected value of their temporal diameter. We then provide a partial characterization of fast random temporal networks. We also define the critical availability as a measure of periodic random availability of the links of a network, required to make the network fast. We finally give a lower bound as well as an upper bound on the (critical) availability.},
pages = {109--120},
journaltitle = {Journal of Parallel and Distributed Computing},
shortjournal = {Journal of Parallel and Distributed Computing},
author = {Akrida, Eleni C. and Gąsieniec, Leszek and Mertzios, George B. and Spirakis, Paul G.},
urldate = {2018-02-22},
date = {2016-01-01},
keywords = {Availability, Diameter, Random input, Temporal networks},
file = {10.1.1.721.6341.pdf:/home/dimitri/Zotero/storage/RJU2GI5T/10.1.1.721.6341.pdf:application/pdf;ScienceDirect Snapshot:/home/dimitri/Zotero/storage/6NLW8PWX/S0743731515001872.html:text/html}
}
@article{benson_simplicial_2018,
title = {Simplicial Closure and Higher-order Link Prediction},
url = {http://arxiv.org/abs/1802.06916},
abstract = {Networks provide a powerful formalism for modeling complex systems, by representing the underlying set of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to-person, collaboration among a team rather than a pair of co-authors, or biological interaction between a set of molecules rather than just two. We refer to these type of simultaneous interactions on sets of more than two nodes as higher-order interactions; they are ubiquitous, but the empirical study of them has lacked a general framework for evaluating higher-order models. Here we introduce such a framework, based on link prediction, a fundamental problem in network analysis. The traditional link prediction problem seeks to predict the appearance of new links in a network, and here we adapt it to predict which (larger) sets of elements will have future interactions. We study the temporal evolution of 19 datasets from a variety of domains, and use our higher-order formulation of link prediction to assess the types of structural features that are most predictive of new multi-way interactions. Among our results, we find that different domains vary considerably in their distribution of higher-order structural parameters, and that the higher-order link prediction problem exhibits some fundamental differences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.},
journaltitle = {{arXiv}:1802.06916 [cond-mat, physics:physics, stat]},
author = {Benson, Austin R. and Abebe, Rediet and Schaub, Michael T. and Jadbabaie, Ali and Kleinberg, Jon},
urldate = {2018-02-27},
date = {2018-02-19},
eprinttype = {arxiv},
eprint = {1802.06916},
keywords = {Statistics - Machine Learning, Mathematics - Algebraic Topology, Physics - Physics and Society, Computer Science - Social and Information Networks, Condensed Matter - Statistical Mechanics},
file = {arXiv\:1802.06916 PDF:/home/dimitri/Zotero/storage/C5IG7QGL/Benson et al. - 2018 - Simplicial Closure and Higher-order Link Predictio.pdf:application/pdf}
}
@article{mellor_temporal_2017,
title = {The Temporal Event Graph},
issn = {2051-1310, 2051-1329},
url = {http://arxiv.org/abs/1706.02128},
doi = {10.1093/comnet/cnx048},
abstract = {Temporal networks are increasingly being used to model the interactions of complex systems. Most studies require the temporal aggregation of edges (or events) into discrete time steps to perform analysis. In this article we describe a static, lossless, and unique representation of a temporal network, the temporal event graph ({TEG}). The {TEG} describes the temporal network in terms of both the inter-event time and two-event temporal motif distributions. By considering these distributions in unison we provide a new method to characterise the behaviour of individuals and collectives in temporal networks as well as providing a natural decomposition of the network. We illustrate the utility of the {TEG} by providing examples on both synthetic and real temporal networks.},
journaltitle = {Journal of Complex Networks},
author = {Mellor, Andrew},
urldate = {2018-02-27},
date = {2017-10-06},
eprinttype = {arxiv},
eprint = {1706.02128},
keywords = {Physics - Physics and Society, Computer Science - Social and Information Networks, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Physics - Data Analysis, Statistics and Probability},
file = {arXiv\:1706.02128 PDF:/home/dimitri/Zotero/storage/6HQ7IV56/Mellor - 2017 - The Temporal Event Graph.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/QGSF97W4/1706.html:text/html}
}
@article{oh_complex_2017,
title = {Complex Contagions with Timers},
url = {http://arxiv.org/abs/1706.04252},
abstract = {A great deal of effort has gone into trying to model social influence --- including the spread of behavior, norms, and ideas --- on networks. Most models of social influence tend to assume that individuals react to changes in the states of their neighbors without any time delay, but this is often not true in social contexts, where (for various reasons) different agents can have different response times. To examine such situations, we introduce the idea of a timer into threshold models of social influence. The presence of timers on nodes delays the adoption --- i.e., change of state --- of each agent, which in turn delays the adoptions of its neighbors. With a homogeneous-distributed timer, in which all nodes exhibit the same amount of delay, adoption delays are also homogeneous, so the adoption order of nodes remains the same. However, heterogeneously-distributed timers can change the adoption order of nodes and hence the "adoption paths" through which state changes spread in a network. Using a threshold model of social contagions, we illustrate that heterogeneous timers can either accelerate or decelerate the spread of adoptions compared to an analogous situation with homogeneous timers, and we investigate the relationship of such acceleration or deceleration with respect to timer distribution and network structure. We derive an analytical approximation for the temporal evolution of the fraction of adopters by modifying a pair approximation of the Watts threshold model, and we find good agreement with numerical computations. We also examine our new timer model on networks constructed from empirical data.},
journaltitle = {{arXiv}:1706.04252 [nlin, physics:physics]},
author = {Oh, Se-Wook and Porter, Mason A.},
urldate = {2018-02-27},
date = {2017-06-13},
eprinttype = {arxiv},
eprint = {1706.04252},
keywords = {Mathematics - Probability, Physics - Physics and Society, Computer Science - Social and Information Networks, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Mathematics - Dynamical Systems},
file = {arXiv\:1706.04252 PDF:/home/dimitri/Zotero/storage/DC3LZPEC/Oh and Porter - 2017 - Complex Contagions with Timers.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/6FT2IFSL/1706.html:text/html}
}
@article{mellor_classifying_2018,
title = {Classifying Conversation in Digital Communication},
url = {http://arxiv.org/abs/1801.10527},
abstract = {Many studies of digital communication, in particular of Twitter, use natural language processing ({NLP}) to find topics, assess sentiment, and describe user behaviour. In finding topics often the relationships between users who participate in the topic are neglected. We propose a novel method of describing and classifying online conversations using only the structure of the underlying temporal network and not the content of individual messages. This method utilises all available information in the temporal network (no aggregation), combining both topological and temporal structure using temporal motifs and inter-event times. This allows us create an embedding of the temporal network in order to describe the behaviour of individuals and collectives over time and examine the structure of conversation over multiple timescales.},
journaltitle = {{arXiv}:1801.10527 [nlin, physics:physics]},
author = {Mellor, Andrew},
urldate = {2018-02-27},
date = {2018-01-31},
eprinttype = {arxiv},
eprint = {1801.10527},
keywords = {Physics - Physics and Society, Computer Science - Social and Information Networks, Nonlinear Sciences - Adaptation and Self-Organizing Systems},
file = {arXiv\:1801.10527 PDF:/home/dimitri/Zotero/storage/XZ25JRM6/Mellor - 2018 - Classifying Conversation in Digital Communication.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/YWMLZBQ8/1801.html:text/html}
}
@article{peel_multiscale_2017,
title = {Multiscale mixing patterns in networks},
url = {http://arxiv.org/abs/1708.01236},
abstract = {Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with the same age, race, or political belief. Quantifying the level of assortativity or disassortativity (the preference of linking to nodes with different attributes) can shed light on the factors involved in the formation of links and contagion processes in complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of discrete-valued metadata. This global value is the average level of assortativity across the network and may not be a representative statistic when mixing patterns are heterogeneous. For example, a social network spanning the globe may exhibit local differences in mixing patterns as a consequence of differences in cultural norms. Here, we introduce an approach to localise this global measure so that we can describe the assortativity, across multiple scales, at the node level. Consequently we are able to capture and qualitatively evaluate the distribution of mixing patterns in the network. We find that for many real-world networks the distribution of assortativity is skewed, overdispersed and multimodal. Our method provides a clearer lens through which we can more closely examine mixing patterns in networks.},
journaltitle = {{arXiv}:1708.01236 [physics]},
author = {Peel, Leto and Delvenne, Jean-Charles and Lambiotte, Renaud},
urldate = {2018-02-27},
date = {2017-08-03},
eprinttype = {arxiv},
eprint = {1708.01236},
keywords = {Physics - Physics and Society, Computer Science - Social and Information Networks, Physics - Data Analysis, Statistics and Probability},
file = {arXiv\:1708.01236 PDF:/home/dimitri/Zotero/storage/YDCIYN5C/Peel et al. - 2017 - Multiscale mixing patterns in networks.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/6YUS3U3T/1708.html:text/html}
}
@article{cang_evolutionary_2018,
title = {Evolutionary homology on coupled dynamical systems},
url = {http://arxiv.org/abs/1802.04677},
abstract = {Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze the topological persistence over spatial scales, persistent homology has rarely been devised for time evolution. We propose the use of a new filtration function for persistent homology which takes as input the adjacent oscillator trajectories of a dynamical system. We also regulate the dynamical system by a weighted graph Laplacian matrix derived from the network of interest, which embeds the topological connectivity of the network into the dynamical system. The resulting topological signatures, which we call evolutionary homology ({EH}) barcodes, reveal the topology-function relationship of the network and thus give rise to the quantitative analysis of nodal properties. The proposed {EH} is applied to protein residue networks for protein thermal fluctuation analysis, rendering the most accurate B-factor prediction of a set of 364 proteins. This work extends the utility of dynamical systems to the quantitative modeling and analysis of realistic physical systems.},
journaltitle = {{arXiv}:1802.04677 [math, q-bio]},
author = {Cang, Zixuan and Munch, Elizabeth and Wei, Guo-Wei},
urldate = {2018-04-05},
date = {2018-02-13},
eprinttype = {arxiv},
eprint = {1802.04677},
keywords = {Mathematics - Algebraic Topology, Mathematics - Dynamical Systems, Quantitative Biology - Quantitative Methods},
file = {arXiv\:1802.04677 PDF:/home/dimitri/Zotero/storage/4TZC2U2K/Cang et al. - 2018 - Evolutionary homology on coupled dynamical systems.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/IR4MU62L/1802.html:text/html}
}
@article{bazzi_generative_2016,
title = {Generative Benchmark Models for Mesoscale Structure in Multilayer Networks},
url = {http://arxiv.org/abs/1608.06196},
abstract = {Multilayer networks allow one to represent diverse and interdependent connectivity patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate "mesoscale" (i.e., intermediate-scale) structures, such as dense sets of nodes known as "communities" that are connected sparsely to each other, to discover network features that are not apparent at the microscale or the macroscale. A variety of methods and algorithms are available to identify communities in multilayer networks, but they differ in their definitions and/or assumptions of what constitutes a community, and many scalable algorithms provide approximate solutions with little or no theoretical guarantee on the quality of their approximations. Consequently, it is crucial to develop generative models of networks to use as a common test of community-detection tools. In the present paper, we develop a family of benchmarks for detecting mesoscale structures in multilayer networks by introducing a generative model that can explicitly incorporate dependency structure between layers. Our benchmark provides a standardized set of null models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. We discuss the parameters and properties of our generative model, and we illustrate its use by comparing a variety of community-detection methods.},
journaltitle = {{arXiv}:1608.06196 [cond-mat, physics:nlin, physics:physics, stat]},
author = {Bazzi, Marya and Jeub, Lucas G. S. and Arenas, Alex and Howison, Sam D. and Porter, Mason A.},
urldate = {2018-04-30},
date = {2016-08-22},
eprinttype = {arxiv},
eprint = {1608.06196},
keywords = {Physics - Physics and Society, Statistics - Methodology, Computer Science - Social and Information Networks, Condensed Matter - Statistical Mechanics, Nonlinear Sciences - Adaptation and Self-Organizing Systems},
file = {arXiv\:1608.06196 PDF:/home/dimitri/Zotero/storage/LRM9HWTC/Bazzi et al. - 2016 - Generative Benchmark Models for Mesoscale Structur.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/JM7VWEGD/1608.html:text/html}
}
@article{sekara_fundamental_2016,
title = {Fundamental structures of dynamic social networks},
volume = {113},
rights = {© . Freely available online through the {PNAS} open access option.},
issn = {0027-8424, 1091-6490},
url = {http://www.pnas.org/content/113/36/9977},
doi = {10.1073/pnas.1602803113},
abstract = {Social systems are in a constant state of flux, with dynamics spanning from minute-by-minute changes to patterns present on the timescale of years. Accurate models of social dynamics are important for understanding the spreading of influence or diseases, formation of friendships, and the productivity of teams. Although there has been much progress on understanding complex networks over the past decade, little is known about the regularities governing the microdynamics of social networks. Here, we explore the dynamic social network of a densely-connected population of ∼1,000 individuals and their interactions in the network of real-world person-to-person proximity measured via Bluetooth, as well as their telecommunication networks, online social media contacts, geolocation, and demographic data. These high-resolution data allow us to observe social groups directly, rendering community detection unnecessary. Starting from 5-min time slices, we uncover dynamic social structures expressed on multiple timescales. On the hourly timescale, we find that gatherings are fluid, with members coming and going, but organized via a stable core of individuals. Each core represents a social context. Cores exhibit a pattern of recurring meetings across weeks and months, each with varying degrees of regularity. Taken together, these findings provide a powerful simplification of the social network, where cores represent fundamental structures expressed with strong temporal and spatial regularity. Using this framework, we explore the complex interplay between social and geospatial behavior, documenting how the formation of cores is preceded by coordination behavior in the communication networks and demonstrating that social behavior can be predicted with high precision.},
pages = {9977--9982},
number = {36},
journaltitle = {Proceedings of the National Academy of Sciences},
shortjournal = {{PNAS}},
author = {Sekara, Vedran and Stopczynski, Arkadiusz and Lehmann, Sune},
urldate = {2018-04-30},
date = {2016-09-06},
langid = {english},
pmid = {27555584},
keywords = {complex networks, computational social science, human dynamics, human mobility, social systems},
file = {Full Text PDF:/home/dimitri/Zotero/storage/XX3SU37E/Sekara et al. - 2016 - Fundamental structures of dynamic social networks.pdf:application/pdf;pnas.1602803113.sapp.pdf:/home/dimitri/Zotero/storage/IV3NN8R3/pnas.1602803113.sapp.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/WIREJBWU/9977.html:text/html}
}
@article{peel_detecting_2014,
title = {Detecting change points in the large-scale structure of evolving networks},
url = {http://arxiv.org/abs/1403.0989},
abstract = {Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks.},
journaltitle = {{arXiv}:1403.0989 [physics, stat]},
author = {Peel, Leto and Clauset, Aaron},
urldate = {2018-04-30},
date = {2014-03-04},
eprinttype = {arxiv},
eprint = {1403.0989},
keywords = {Statistics - Machine Learning, Physics - Physics and Society, Computer Science - Social and Information Networks},
file = {arXiv\:1403.0989 PDF:/home/dimitri/Zotero/storage/4DBDLPT3/Peel and Clauset - 2014 - Detecting change points in the large-scale structu.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/4IGGSISH/1403.html:text/html}
}
@article{gauvin_randomized_2018,
title = {Randomized reference models for temporal networks},
url = {http://arxiv.org/abs/1806.04032},
abstract = {Many real-world dynamical systems can successfully be analyzed using the temporal network formalism. Empirical temporal networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated dynamics, making their analysis particularly challenging. Randomized reference models ({RRMs}) for temporal networks constitute a versatile toolbox for studying such systems. Defined as ensembles of random networks with given features constrained to match those of an input (empirical) network, they may be used to identify statistically significant motifs in empirical temporal networks (i.e. overrepresented w.r.t. the null random networks) and to infer the effects of such motifs on dynamical processes unfolding in the network. However, the effects of most randomization procedures on temporal network characteristics remain poorly understood, rendering their use non-trivial and susceptible to misinterpretation. Here we propose a unified framework for classifying and understanding microcanonical {RRMs} ({MRRMs}). We use this framework to propose a canonical naming convention for existing randomization procedures, classify them, and deduce their effects on a range of important temporal network features. We furthermore show that certain classes of compatible {MRRMs} may be applied in sequential composition to generate more than a hundred new {MRRMs} from existing ones surveyed in this article. We provide a tutorial for the use of {MRRMs} to analyze an empirical temporal network and we review applications of {MRRMs} found in literature. The taxonomy of {MRRMs} we have developed provides a reference to ease the use of {MRRMs}, and the theoretical foundations laid here may further serve as a base for the development of a principled and systematic way to generate and apply randomized reference null models for the study of temporal networks.},
journaltitle = {{arXiv}:1806.04032 [physics, q-bio]},
author = {Gauvin, Laetitia and Génois, Mathieu and Karsai, Márton and Kivelä, Mikko and Takaguchi, Taro and Valdano, Eugenio and Vestergaard, Christian L.},
urldate = {2018-06-14},
date = {2018-06-11},
eprinttype = {arxiv},
eprint = {1806.04032},
keywords = {Physics - Physics and Society, Physics - Data Analysis, Statistics and Probability, Quantitative Biology - Quantitative Methods, Computer Science - Discrete Mathematics},
file = {arXiv\:1806.04032 PDF:/home/dimitri/Zotero/storage/GVBEMC2A/Gauvin et al. - 2018 - Randomized reference models for temporal networks.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/8WF5HVDE/1806.html:text/html}
}
@article{liu_eses:_2017,
title = {{ESES}: Software for Eulerian solvent excluded surface},
volume = {38},
issn = {1096-987X},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.24682},
doi = {10.1002/jcc.24682},
shorttitle = {{ESES}},
pages = {446--466},
number = {7},
journaltitle = {Journal of Computational Chemistry},
author = {Liu, Beibei and Wang, Bao and Zhao, Rundong and Tong, Yiying and Wei, Guo-Wei},
urldate = {2018-06-18},
date = {2017-01-04},
langid = {english},
file = {Liu et al. - 2017 - ESES Software for Eulerian solvent excluded surfa.pdf:/home/dimitri/Zotero/storage/M3TJKX6T/Liu et al. - 2017 - ESES Software for Eulerian solvent excluded surfa.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/ULYNDKZZ/jcc.html:text/html}
}
@article{petri_simplicial_2018,
title = {Simplicial Activity Driven Model},
url = {http://arxiv.org/abs/1805.06740},
abstract = {Many complex systems find a convenient representation in terms of networks: structures made by pairwise interactions of elements. Their evolution is often described by temporal networks, in which links between two nodes are replaced by sequences of events describing how interactions change over time. In particular, the Activity-Driven ({AD}) model has been widely considered, as the simplicity of its definition allows for analytical insights and various refinements. For many biological and social systems however, elementary interactions involve however more than two elements, and structures such as simplicial complexes are more adequate to describe such phenomena. Here, we propose a Simplicial Activity Driven ({SAD}) model in which the building block is a simplex of nodes representing a multi-agent interaction, instead of a set of binary interactions. We compare the resulting system with {AD} models with the same numbers of events. We highlight the resulting structural differences and show analytically and numerically that the simplicial structure leads to crucial differences in the outcome of paradigmatic processes modelling disease propagation or social contagion.},
journaltitle = {{arXiv}:1805.06740 [physics]},
author = {Petri, Giovanni and Barrat, Alain},
urldate = {2018-06-18},
date = {2018-05-17},
eprinttype = {arxiv},
eprint = {1805.06740},
keywords = {Physics - Physics and Society},
file = {arXiv\:1805.06740 PDF:/home/dimitri/Zotero/storage/XJANUF3F/Petri and Barrat - 2018 - Simplicial Activity Driven Model.pdf:application/pdf;arXiv.org Snapshot:/home/dimitri/Zotero/storage/FQ3TYRYA/1805.html:text/html}
}
@article{bassett_network_2017,
title = {Network neuroscience},
volume = {20},
rights = {2017 Nature Publishing Group},
issn = {1546-1726},
url = {https://www.nature.com/articles/nn.4502},
doi = {10.1038/nn.4502},
abstract = {Despite substantial recent progress, our understanding of the principles and mechanisms underlying complex brain function and cognition remains incomplete. Network neuroscience proposes to tackle these enduring challenges. Approaching brain structure and function from an explicitly integrative perspective, network neuroscience pursues new ways to map, record, analyze and model the elements and interactions of neurobiological systems. Two parallel trends drive the approach: the availability of new empirical tools to create comprehensive maps and record dynamic patterns among molecules, neurons, brain areas and social systems; and the theoretical framework and computational tools of modern network science. The convergence of empirical and computational advances opens new frontiers of scientific inquiry, including network dynamics, manipulation and control of brain networks, and integration of network processes across spatiotemporal domains. We review emerging trends in network neuroscience and attempt to chart a path toward a better understanding of the brain as a multiscale networked system.},
pages = {353--364},
number = {3},
journaltitle = {Nature Neuroscience},
author = {Bassett, Danielle S. and Sporns, Olaf},
urldate = {2018-07-10},
date = {2017-03},
langid = {english},
file = {Bassett and Sporns - 2017 - Network neuroscience.pdf:/home/dimitri/Zotero/storage/8H5EDRXQ/Bassett and Sporns - 2017 - Network neuroscience.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/E92MLVZA/nn.html:text/html}
}
@article{newman_network_2018,
title = {Network structure from rich but noisy data},
volume = {14},
rights = {2018 The Author(s)},
issn = {1745-2481},
url = {https://www.nature.com/articles/s41567-018-0076-1},
doi = {10.1038/s41567-018-0076-1},
abstract = {A technique allows optimal inference of the structure of a network when the available observed data are rich but noisy, incomplete or otherwise unreliable.},
pages = {542--545},
number = {6},
journaltitle = {Nature Physics},
author = {Newman, M. E. J.},
urldate = {2018-07-10},
date = {2018-06},
langid = {english},
file = {Full Text PDF:/home/dimitri/Zotero/storage/F8AYYMEJ/Newman - 2018 - Network structure from rich but noisy data.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/MIZRK2YS/s41567-018-0076-1.html:text/html}
}
@article{eagle_reality_2006,
title = {Reality mining: sensing complex social systems},
volume = {10},
issn = {1617-4909, 1617-4917},
url = {https://link.springer.com/article/10.1007/s00779-005-0046-3},
doi = {10.1007/s00779-005-0046-3},
shorttitle = {Reality mining},
abstract = {We introduce a system for sensing complex social systems with data collected from 100 mobile phones over the course of 9 months. We demonstrate the ability to use standard Bluetooth-enabled mobile telephones to measure information access and use in different contexts, recognize social patterns in daily user activity, infer relationships, identify socially significant locations, and model organizational rhythms.},
pages = {255--268},
number = {4},
journaltitle = {Personal and Ubiquitous Computing},
shortjournal = {Pers Ubiquit Comput},
author = {Eagle, Nathan and Pentland, Alex (Sandy)},
urldate = {2018-07-23},
date = {2006-05-01},
langid = {english},
file = {Eagle and Pentland - 2006 - Reality mining sensing complex social systems.pdf:/home/dimitri/Zotero/storage/H9DUQJ6T/Eagle and Pentland - 2006 - Reality mining sensing complex social systems.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/8DH79ULJ/10.html:text/html}
}

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