7 Search Results for "Carri�re, Mathieu"

Document
DOI: 10.4230/LIPIcs.SoCG.2020.11
Persistent Homology Based Characterization of the Breast Cancer Immune Microenvironment: A Feasibility Study

Authors: Andrew Aukerman, Mathieu Carrière, Chao Chen, Kevin Gardner, Raúl Rabadán, and Rami Vanguri

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
Persistent homology is a common tool of topological data analysis, whose main descriptor, the persistence diagram, aims at computing and encoding the geometry and topology of given datasets. In this article, we present a novel application of persistent homology to characterize the spatial arrangement of immune and epithelial (tumor) cells within the breast cancer immune microenvironment. More specifically, quantitative and robust characterizations are built by computing persistence diagrams out of a staining technique (quantitative multiplex immunofluorescence) which allows us to obtain spatial coordinates and stain intensities on individual cells. The resulting persistence diagrams are evaluated as characteristic biomarkers of cancer subtype and prognostic biomarker of overall survival. For a cohort of approximately 700 breast cancer patients with median 8.5-year clinical follow-up, we show that these persistence diagrams outperform and complement the usual descriptors which capture spatial relationships with nearest neighbor analysis. This provides new insights and possibilities on the general problem of building (topology-based) biomarkers that are characteristic and predictive of cancer subtype, overall survival and response to therapy.
Cite as

Andrew Aukerman, Mathieu Carrière, Chao Chen, Kevin Gardner, Raúl Rabadán, and Rami Vanguri. Persistent Homology Based Characterization of the Breast Cancer Immune Microenvironment: A Feasibility Study. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aukerman_et_al:LIPIcs.SoCG.2020.11,
  author =	{Aukerman, Andrew and Carri\`{e}re, Mathieu and Chen, Chao and Gardner, Kevin and Rabad\'{a}n, Ra\'{u}l and Vanguri, Rami},
  title =	{{Persistent Homology Based Characterization of the Breast Cancer Immune Microenvironment: A Feasibility Study}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.11},
  URN =		{urn:nbn:de:0030-drops-121695},
  doi =		{10.4230/LIPIcs.SoCG.2020.11},
  annote =	{Keywords: Topological data analysis, persistence diagrams}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.21
On the Metric Distortion of Embedding Persistence Diagrams into Separable Hilbert Spaces

Authors: Mathieu Carrière and Ulrich Bauer

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their diagram distances, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of persistence diagrams into Reproducing Kernel Hilbert Spaces, in which all computations can be performed easily. Since persistence diagrams enjoy theoretical stability guarantees for the diagram distances, the metric properties of the feature map, i.e., the relationship between the Hilbert distance and the diagram distances, are of central interest for understanding if the persistence diagram guarantees carry over to the embedding. In this article, we study the possibility of embedding persistence diagrams into separable Hilbert spaces with bi-Lipschitz maps. In particular, we show that for several stable embeddings into infinite-dimensional Hilbert spaces defined in the literature, any lower bound must depend on the cardinalities of the persistence diagrams, and that when the Hilbert space is finite dimensional, finding a bi-Lipschitz embedding is impossible, even when restricting the persistence diagrams to have bounded cardinalities.
Cite as

Mathieu Carrière and Ulrich Bauer. On the Metric Distortion of Embedding Persistence Diagrams into Separable Hilbert Spaces. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{carriere_et_al:LIPIcs.SoCG.2019.21,
  author =	{Carri\`{e}re, Mathieu and Bauer, Ulrich},
  title =	{{On the Metric Distortion of Embedding Persistence Diagrams into Separable Hilbert Spaces}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.21},
  URN =		{urn:nbn:de:0030-drops-104259},
  doi =		{10.4230/LIPIcs.SoCG.2019.21},
  annote =	{Keywords: Topological Data Analysis, Persistence Diagrams, Hilbert space embedding}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.47
The Flow of Information in Interactive Quantum Protocols: the Cost of Forgetting

Authors: Mathieu Laurière and Dave Touchette

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
In two-party interactive quantum communication protocols, we study a recently defined notion of quantum information cost (QIC), which has most of the important properties of its classical analogue (IC). Notably, its link with amortized quantum communication complexity has been used to prove an (almost) tight lower bound on the bounded round quantum complexity of Disjointness. However, QIC was defined through a purification of the input state. This is valid for fully quantum inputs and tasks but difficult to interpret even for classical tasks. Also, its link with other notions of information cost that had appeared in the literature was not clear. We settle both these issues: for quantum communication with classical inputs, we characterize QIC in terms of information about the input registers, avoiding any reference to the notion of a purification of the classical input state. We provide an operational interpretation of this new characterization as the sum of the costs of revealing and of forgetting information about the inputs. To obtain this result, we prove a general Information Flow Lemma assessing the transfer of information in general interactive quantum processes. Specializing this lemma to interactive quantum protocols accomplishing classical tasks, we are able to demistify the link between QIC and other previous notions of information cost in quantum protocols. Furthermore, we clarify the link between QIC and IC by simulating quantumly classical protocols. Finally, we apply these concepts to argue that any quantum protocol that does not forget information solves Disjointness on n-bits in Omega(n) communication, completely losing the quadratic quantum speedup. Hence forgetting information is here a necessary feature in order to obtain any significant improvement over classical protocols. We also prove that QIC at 0-error is exactly n for Inner Product, and n (1 - o(1)) for a random Boolean function on n+n bits.
Cite as

Mathieu Laurière and Dave Touchette. The Flow of Information in Interactive Quantum Protocols: the Cost of Forgetting. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, p. 47:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{lauriere_et_al:LIPIcs.ITCS.2017.47,
  author =	{Lauri\`{e}re, Mathieu and Touchette, Dave},
  title =	{{The Flow of Information in Interactive Quantum Protocols: the Cost of Forgetting}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{47:1--47:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.47},
  URN =		{urn:nbn:de:0030-drops-81898},
  doi =		{10.4230/LIPIcs.ITCS.2017.47},
  annote =	{Keywords: Communication Complexity, Information Complexity, Quantum Computation and Information}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2017.25
Local Equivalence and Intrinsic Metrics between Reeb Graphs

Authors: Mathieu Carrière and Steve Oudot

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for applications, where it matters to quantify the extent by which two given Reeb graphs differ. Recent contributions emphasize this aspect, proposing novel distances such as functional distortion or interleaving that are provably more discriminative than the so-called bottleneck distance, being true metrics whereas the latter is only a pseudo-metric. Their main drawback compared to the bottleneck distance is to be comparatively hard (if at all possible) to evaluate. Here we take the opposite view on the problem and show that the bottleneck distance is in fact good enough locally, in the sense that it is able to discriminate a Reeb graph from any other Reeb graph in a small enough neighborhood, as efficiently as the other metrics do. This suggests considering the intrinsic metrics induced by these distances, which turn out to be all globally equivalent. This novel viewpoint on the study of Reeb graphs has a potential impact on applications, where one may not only be interested in discriminating between data but also in interpolating between them.
Cite as

Mathieu Carrière and Steve Oudot. Local Equivalence and Intrinsic Metrics between Reeb Graphs. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{carriere_et_al:LIPIcs.SoCG.2017.25,
  author =	{Carri\`{e}re, Mathieu and Oudot, Steve},
  title =	{{Local Equivalence and Intrinsic Metrics between Reeb Graphs}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{25:1--25:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.25},
  URN =		{urn:nbn:de:0030-drops-71794},
  doi =		{10.4230/LIPIcs.SoCG.2017.25},
  annote =	{Keywords: Reeb Graphs, Extended Persistence, Induced Metrics, Topological Data Analysis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.20
Extended Learning Graphs for Triangle Finding

Authors: Titouan Carette, Mathieu Laurière, and Frédéric Magniez

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
We present new quantum algorithms for Triangle Finding improving its best previously known quantum query complexities for both dense and sparse instances. For dense graphs on n vertices, we get a query complexity of O(n^(5/4)) without any of the extra logarithmic factors present in the previous algorithm of Le Gall [FOCS'14]. For sparse graphs with m >= n^(5/4) edges, we get a query complexity of O(n^(11/12) m^(1/6) sqrt(log n)), which is better than the one obtained by Le Gall and Nakajima [ISAAC'15] when m >= n^(3/2). We also obtain an algorithm with query complexity O(n^(5/6) (m log n)^(1/6) + d_2 sqrt(n)) where d_2 is the variance of the degree distribution. Our algorithms are designed and analyzed in a new model of learning graphs that we call extended learning graphs. In addition, we present a framework in order to easily combine and analyze them. As a consequence we get much simpler algorithms and analyses than previous algorithms of Le Gall based on the MNRS quantum walk framework [SICOMP'11].
Cite as

Titouan Carette, Mathieu Laurière, and Frédéric Magniez. Extended Learning Graphs for Triangle Finding. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{carette_et_al:LIPIcs.STACS.2017.20,
  author =	{Carette, Titouan and Lauri\`{e}re, Mathieu and Magniez, Fr\'{e}d\'{e}ric},
  title =	{{Extended Learning Graphs for Triangle Finding}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.20},
  URN =		{urn:nbn:de:0030-drops-70132},
  doi =		{10.4230/LIPIcs.STACS.2017.20},
  annote =	{Keywords: Quantum query complexity, learning graphs, triangle finding}
}
Document
DOI: 10.4230/LIPIcs.TQC.2016.5
Robust Bell Inequalities from Communication Complexity

Authors: Sophie Laplante, Mathieu Laurière, Alexandre Nolin, Jérémie Roland, and Gabriel Senno

Published in: LIPIcs, Volume 61, 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)

Abstract
The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bounds. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities.
Cite as

Sophie Laplante, Mathieu Laurière, Alexandre Nolin, Jérémie Roland, and Gabriel Senno. Robust Bell Inequalities from Communication Complexity. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{laplante_et_al:LIPIcs.TQC.2016.5,
  author =	{Laplante, Sophie and Lauri\`{e}re, Mathieu and Nolin, Alexandre and Roland, J\'{e}r\'{e}mie and Senno, Gabriel},
  title =	{{Robust Bell Inequalities from Communication Complexity}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.5},
  URN =		{urn:nbn:de:0030-drops-66867},
  doi =		{10.4230/LIPIcs.TQC.2016.5},
  annote =	{Keywords: Communication complexity, Bell inequalities, nonlocality, detector efficiency}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.25
Structure and Stability of the 1-Dimensional Mapper

Authors: Mathieu Carrière and Steve Oudot

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
Given a continuous function f:X->R and a cover I of its image by intervals, the Mapper is the nerve of a refinement of the pullback cover f^{-1}(I). Despite its success in applications, little is known about the structure and stability of this construction from a theoretical point of view. As a pixelized version of the Reeb graph of f, it is expected to capture a subset of its features (branches, holes), depending on how the interval cover is positioned with respect to the critical values of the function. Its stability should also depend on this positioning. We propose a theoretical framework relating the structure of the Mapper to that of the Reeb graph, making it possible to predict which features will be present and which will be absent in the Mapper given the function and the cover, and for each feature, to quantify its degree of (in-)stability. Using this framework, we can derive guarantees on the structure of the Mapper, on its stability, and on its convergence to the Reeb graph as the granularity of the cover I goes to zero.
Cite as

Mathieu Carrière and Steve Oudot. Structure and Stability of the 1-Dimensional Mapper. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{carriere_et_al:LIPIcs.SoCG.2016.25,
  author =	{Carri\`{e}re, Mathieu and Oudot, Steve},
  title =	{{Structure and Stability of the 1-Dimensional Mapper}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.25},
  URN =		{urn:nbn:de:0030-drops-59175},
  doi =		{10.4230/LIPIcs.SoCG.2016.25},
  annote =	{Keywords: Mapper, Reeb Graph, Extended Persistence, Topological Data Analysis}
}
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