2025Activity reportProject-Team​​DATASHAPE

7.1.1 GUDHI

• Name:​​​‌
  Geometric Understanding in Higher​ Dimensions
• Keywords:
  Computational geometry,​‌ Topology, Clustering
• Scientific Description:​​

  The Gudhi library is​​​‌ an open source library​ for Computational Topology and​‌ Topological Data Analysis (TDA).​​ It offers state-of-the-art algorithms​​​‌ to construct various types​ of simplicial complexes, data​‌ structures to represent them,​​ and algorithms to compute​​​‌ geometric approximations of shapes​ and persistent homology.

  The​‌ GUDHI library offers the​​ following interoperable modules:

  .​​​‌ Complexes: + Cubical +​ Simplicial: Rips, Witness, Alpha​‌ and Čech complexes +​​ Cover: Nerve and Graph​​​‌ induced complexes . Data​ structures and basic operations:​‌ + Simplex tree, Skeleton​​ blockers and Toplex map​​​‌ + Construction, update, filtration​ and simplification . Topological​‌ descriptors computation . Manifold​​ reconstruction . Topological descriptors​​​‌ tools: + Bottleneck and​ Wasserstein distance + Statistical​‌ tools + Persistence diagram​​ and barcode

• Functional Description:​​​‌
  The GUDHI open source​ library will provide the​‌ central data structures and​​ algorithms that underly applications​​​‌ in geometry understanding in​ higher dimensions. It is​‌ intended to both help​​ the development of new​​​‌ algorithmic solutions inside and​ outside the project, and​‌ to facilitate the transfer​​ of results in applied​​​‌ fields.
• News of the​ Year:

  Below is a​‌ list of changes made​​ since GUDHI 3.10.1:

  -​​​‌ Delaunay complex . The​ Delaunay complex can be​‌ equipped with different filtrations:​​ * Delaunay complex (no​​​‌ filtration values computed) *​ Delaunay-Čech complex (using minimal​‌ enclosing ball) * Alpha​​ complex (moved in this​​​‌ new section) . The​ Delaunay-Čech and Alpha complex​‌ can output square, or​​ not square, filtration values​​​‌ . An incremental version​ of the Delaunay complex​‌ (only in C++)

  -​​ Rips complex persistence scikit-learn​​​‌ like interface . A​ binding to Ripser when​‌ it accelerates the computation​​

  - Persistence graphical tools​​​‌ . Can now handle​ scikit-learn like interfaces outputs​‌ as inputs

  - Simplex​​ tree . Can now​​​‌ store additionnal data on​ each simplex (only in​‌ C++) . Can be​​ const

• URL:
  https://­gudhi.­inria.­fr/
• Publication:​​​‌
  hal-01108461
• Contact:
  Marc Glisse​
• Participants:
  Marc Glisse, Hannah​‌ Schreiber, 17 anonymous participants​​
• Partners:
  Université Côte d'Azur​​​‌ (UCA), Fujitsu

7.1.2 Multipers​

• Name:
  Multiparameter Persistence for​‌ Machine Learning
• Keywords:
  Topology,​​ Machine learning
• Functional Description:​​​‌
  multipers is a Python​ library for Topological Data​‌ Analysis, focused on Multiparameter​​ Persistence computation and visualizations​​​‌ for Machine Learning. It​ features several efficient computational​‌ and visualization tools, with​​ integrated, easy to use,​​​‌ auto-differentiable Machine Learning pipelines,​ that can be seamlessly​‌ interfaced with scikit-learn and​​ PyTorch. This library is​​ meant to be usable​​​‌ for non-experts in Topological‌ or Geometrical Machine Learning.‌​‌ Performance-critical functions are implemented​​ in C++ or in​​​‌ Cython, are parallelizable with‌ TBB, and have Python‌​‌ bindings and interface. It​​ can handle a very​​​‌ diverse range of datasets‌ that can be framed‌​‌ into a (finite) multi-filtered​​ simplicial or cell complex,​​​‌ including, e.g., point clouds,‌ graphs, time series, images,‌​‌ etc.
• URL:
  https://­davidlapous.­github.­io/­multipers/
• Publication:​​
  hal-04801544
• Contact:
  David Loiseaux​​​‌
• Participants:
  Hannah Schreiber, an‌ anonymous participant

8.1.1 Efficient‌​‌ and Scalable Spatial Regularization​​ of Optimal Transport

Participants:​​​‌ David Cohen-Steiner.

In‌ collaboration with Lucas Brifault‌​‌ (Dassault Systèmes) and Mathieu​​ Desbrun (GEOMERIX)

In this​​​‌ paper (18),‌ we introduce a novel‌​‌ approach to spatial regularization​​ of optimal transport problems.​​​‌ Based on the notion‌ of forward and backward‌​‌ "mean maps" of a​​ transport plan, we introduce​​​‌ a convex formulation of‌ optimal transport problems that‌​‌ incorporates regularization of these​​ mean maps to promote​​​‌ spatial continuity of the‌ resulting optimal plan. Unlike‌​‌ previous regularization approaches that​​ required the optimization of​​​‌ all the transport plan‌ coefficients, our formulation translates‌​‌ into an ADMM-based solver​​ combined with Sinkhorn type​​​‌ algorithms, which drastically reduces‌ the number of variables‌​‌ and scales up to​​ large problems. We demonstrate​​​‌ the usefulness and efficiency‌ of this new computational‌​‌ tool for various applications​​ and for different regularizations.​​​‌

8.1.2 Burning or Collapsing‌ the Medial Axis is‌​‌ Unstable

Participants: Mathijs Wintraecken​​.

In collaboration with​​​‌ Erin Chambers (University of‌ Notre Dame, USA), Christopher‌​‌ Fillmore (Institute of Science​​ and Technology Austria), Elizabeth​​​‌ Stephenson (Orteliu, Oslo, Norway)‌

The medial axis of‌​‌ a set consists of​​ the points in the​​​‌ ambient space without a‌ unique closest point in‌​‌ the original set. Since​​ its introduction, the medial​​​‌ axis has been used‌ extensively in many applications‌​‌ as a method of​​ computing a skeleton topologically​​​‌ equivalent to the original‌ set. Unfortunately, one limiting‌​‌ factor in the use​​ of the medial axis​​​‌ of a smooth manifold‌ is that it is‌​‌ not necessarily topologically stable​​ under small perturbations of​​​‌ the manifold. To counter‌ these instabilities, various prunings‌​‌ of the medial axis​​ have been proposed in​​​‌ the computational geometry community.‌ In this paper (‌​‌12), we examine​​ one type of pruning,​​​‌ called burning. Because of‌ the good experimental results‌​‌ it was hoped that​​ the burning method of​​​‌ simplifying the medial axis‌ would be stable. In‌​‌ this work, we show​​ a simple example that​​​‌ dashes such hopes. Based‌ on Bing's house with‌​‌ two rooms, we demonstrate​​ an isotopy of a​​​‌ shape where the medial‌ axis goes from collapsible‌​‌ to non-collapsible. More precisely,​​ we consider the standard​​​‌ deformation retract from the‌ closed ball to Bing's‌​‌ house with two rooms,​​ but stop just short​​​‌ of the point where‌ Bing's house becomes two‌​‌ dimensional. This way we​​ obtain an isotopy from​​​‌ the 3-ball to a‌ thickened version of Bing's‌​‌ house. Under this isotopy,​​​‌ the medial axis goes​ from collapsible to non-collapsible.​‌ We stress that this​​ isotopy can be made​​​‌ generic, in the sense​ of singularity theory, as​‌ developed by Arnold and​​ Thom.

8.1.3 Sparsification of​​​‌ the generalized persistence diagrams​ for scalability through gradient​‌ descent

Participant: Mathieu Carrière​​.

In collaboration with​​​‌ Seunghyun Kim, Woojin Kim​ (KAIST, South Korea)

In this work,​​​‌ we introduce a novel​ method for optimizing the​‌ domain of the GPD​​ through gradient descent optimization.​​​‌ To achieve this, we​ introduce a loss function​‌ tailored to optimize the​​ selection of intervals, balancing​​​‌ computational efficiency and discriminative​ accuracy. The design of​‌ the loss function is​​ based on the known​​​‌ erosion stability property of​ the GPD. We showcase​‌ the efficiency of our​​ sparsification method for dataset​​​‌ classification in supervised machine​ learning. Experimental results demonstrate​‌ that our sparsification method​​ significantly reduces the time​​​‌ required for computing the​ GPDs associated to several​‌ datasets, while maintaining classification​​ accuracies comparable to those​​​‌ achieved using full GPDs.​ Our method thus opens​‌ the way for the​​ use of GPD-based methods​​​‌ to applications at an​ unprecedented scale.

8.1.4 Multi-parameter​‌ Module Approximation: An Efficient​​ and Interpretable Invariant for​​​‌ Multi-Parameter Persistence Modules with​ Guarantees

Participant: Mathieu Carrière​‌.

In collaboration with​​ David Loiseaux (Inria Saclay)​​​‌ and Andrew J. Blumberg​ (Columbia University, USA)

8.1.5 A​​ fast algorithm for the​​​‌ Hecke representation of the‌ braid group, and applications‌​‌ to the computation of​​ the HOMFLY-PT polynomial and​​​‌ the search for interesting‌ braids

Participant: Clément Maria‌​‌.

In collaboration with​​ Hoel Queffelec (CNRS -​​​‌ Institut Montpelliérain Alexander Grothendieck).‌

Knot theory is an‌​‌ active field of mathematics,​​ in which combinatorial and​​​‌ computational methods play an‌ important role. One side‌​‌ of computational knot theory,​​ that has gained interest​​​‌ in recent years, both‌ for complexity analysis and‌​‌ practical algorithms, is quantum​​ topology and the computation​​​‌ of topological invariants issued‌ from the theory. In‌​‌ this article 40,​​ we leverage the rigidity​​​‌ brought by the representation-theoretic‌ origins of the quantum‌​‌ invariants for algorithmic purposes.​​ We do so by​​​‌ exploiting braids and the‌ algebraic properties of the‌​‌ braid group to describe,​​ analyze, and implement a​​​‌ fast algorithm to compute‌ the Hecke representation of‌​‌ the braid group. We​​ apply this construction to​​​‌ design a parameterized algorithm‌ to compute the HOMFLY-PT‌​‌ polynomial of knots, and​​ demonstrate its interest experimentally.​​​‌ Finally, we combine our‌ fast Hecke representation algorithm‌​‌ with Garside theory, to​​ implement a reservoir sampling​​​‌ search and find non-trivial‌ braids with trivial Hecke‌​‌ representations with coefficients in​​ $\mathbb{Z}/p\mathrm{\mathbb{Z}‌}$. We find several‌ such braids, in particular‌​‌ proving that the Hecke​​ representation of $B_{\mathrm{5‌}}$ with $\mathbb{Z}/\mathrm{2‌}\mathbb{Z}$ coefficients is non-faithful.‌​‌

8.1.6 On Sparse Representations​​ of 3-Manifolds

Participant: Clément​​​‌ Maria.

In collaboration‌ with Kristóf Huszár (TU‌​‌ Graz).

3-manifolds are commonly​​ represented as triangulations, consisting​​​‌ of abstract tetrahedra whose‌ triangular faces are identified‌​‌ in pairs. The combinatorial​​ sparsity of a triangulation,​​​‌ as measured by the‌ treewidth of its dual‌​‌ graph, plays a fundamental​​ role in the design​​​‌ of parameterized algorithms. In‌ this work 36,‌​‌ we investigate algorithmic procedures​​​‌ that transform or modify​ a given triangulation while​‌ controlling specific sparsity parameters.​​ First, we describe a​​​‌ linear-time algorithm that converts​ a given triangulation into​‌ a Heegaard diagram of​​ the underlying 3-manifold, showing​​​‌ that the construction preserves​ treewidth. We apply this​‌ construction to exhibit a​​ fixed-parameter tractable framework for​​​‌ computing Kuperberg's quantum invariants​ of 3-manifolds. Second, we​‌ present a quasi-linear-time algorithm​​ that retriangulates a given​​​‌ triangulation into one with​ maximum edge valence of​‌ at most nine, while​​ only moderately increasing the​​​‌ treewidth of the dual​ graph. Combining these two​‌ algorithms yields a quasi-linear-time​​ algorithm that produces, from​​​‌ a given triangulation, a​ Heegaard diagram in which​‌ every attaching curve intersects​​ at most nine others.​​​‌

8.1.7 Compressed data structures​ for Heegaard splittings

Participant:​‌ Henrique Ennes, Clément​​ Maria.

Heegaard splittings​​​‌ provide a natural representation​ of closed 3-manifolds by​‌ gluing two handlebodies along​​ a common surface. These​​​‌ splittings can be equivalently​ given by two finite​‌ sets of meridians lying​​ on the surface, which​​​‌ define a Heegaard diagram.​ In this work 34​‌, we present a​​ data structure to effectively​​​‌ represent Heegaard diagrams as​ normal curves with respect​‌ to triangulations of a​​ surface, where the complexity​​​‌ is measured by the​ space required to express​‌ the normal coordinates' vectors​​ in binary. This structure​​​‌ can be significantly more​ compact than triangulations of​‌ 3-manifolds, yielding exponential gains​​ for certain families. Even​​​‌ with this succinct definition​ of complexity, we establish​‌ polynomial-time algorithms for comparing​​ and manipulating diagrams, performing​​​‌ stabilizations, detecting trivial stabilizations​ and reductions, and computing​‌ topological invariants of the​​ underlying manifolds, such as​​​‌ their fundamental and homology​ groups. We also contrast​‌ early implementations of our​​ techniques with standard software​​​‌ programs for 3-manifolds, achieving​ faster algorithms for the​‌ average cases and exponential​​ gains in speed for​​​‌ some particular presentations of​ the inputs.

8.1.8 Hardness​‌ of computation of quantum​​ invariants on 3-manifolds with​​​‌ restricted topology

Participant: Henrique​ Ennes, Clément Maria​‌.

Quantum invariants in​​ low dimensional topology offer​​​‌ a wide variety of​ valuable invariants of knots​‌ and 3-manifolds, presented by​​ explicit formulas that are​​​‌ readily computable. Their computational​ complexity has been actively​‌ studied and is tightly​​ connected to topological quantum​​​‌ computing. In this article​ 21, we prove​‌ that for any 3-manifold​​ quantum invariant in the​​​‌ Reshetikhin-Turaev model, there is​ a deterministic polynomial time​‌ algorithm that, given as​​ input an arbitrary closed​​​‌ 3-manifold $M$, outputs​ a closed 3-manifold ${\mathrm{M‌}}^{\text{'}}$ with same quantum​​ invariant, such that ${\mathrm{M‌}}^{\text{'}}$ is hyperbolic, contains​ no low genus embedded​‌ incompressible surface, and is​​ presented by a strongly​​​‌ irreducible Heegaard diagram. Our​ construction relies on properties​‌ of Heegaard splittings and​​ the Hempel distance. At​​​‌ the level of computational​ complexity, this proves that​‌ the hardness of computing​​ a given quantum invariant​​​‌ of 3-manifolds is preserved​ even when severely restricting​‌ the topology and the​​ combinatorics of the input.​​​‌ This positively answers a​ question raised by Samperton.​‌

8.1.9 Well-quasi-orders on embedded​​ planar graphs

Participant: Clément​​ Maria, Corentin Lunel​​​‌.

The central theorem‌ of topological graph theory‌​‌ states that the graph​​ minor relation is a​​​‌ well-quasi-order on graphs. It‌ has far-reaching consequences, in‌​‌ particular in the study​​ of graph structures and​​​‌ the design of (parameterized)‌ algorithms. In this article‌​‌ 39, we study​​ two embedded versions of​​​‌ classical minor relations from‌ structural graph theory and‌​‌ prove that they are​​ also well-quasi-orders on general​​​‌ or restricted classes of‌ embedded planar graphs. These‌​‌ embedded minor relations appear​​ naturally for intrinsically embedded​​​‌ objects, such as knot‌ diagrams and surfaces in‌​‌ ${ℝ}^3$. Handling​​ the extra topological constraints​​​‌ of the embeddings requires‌ careful analysis and extensions‌​‌ of classical methods for​​ the more constrained embedded​​​‌ minor relations. We prove‌ that the embedded version‌​‌ of immersion induces a​​ well-quasi-order on bounded carving-width​​​‌ plane graphs by exhibiting‌ particularly well-structured tree-decompositions and‌​‌ leveraging a classical argument​​ on well-quasi-orders on forests.​​​‌ We deduce that the‌ embedded graph minor relation‌​‌ defines a well-quasi-order on​​ plane graphs via their​​​‌ directed medial graphs, when‌ their branch-width is bounded.‌​‌ We conclude that the​​ embedded graph minor relation​​​‌ is a well-quasi-order on‌ all plane graphs, using‌​‌ classical grids theorems in​​ the unbounded branch-width case.​​​‌

8.1.10 Geometric characterisation of‌ structural and regular equivalences‌​‌ in undirected (hyper)graphs

Participant:​​ Nina Otter.

In​​​‌ collaboration with Marzieh Eidi‌ (MPI MiS).

8.2.1‌​‌ Gromov-Wasserstein Bound between Reeb​​ and Mapper Graphs

Participant:​​​‌ Mathieu Carrière.

In‌ collaboration with Ziyad Oulhaj‌​‌ and Bertrand Michel (École​​ Centrale de Nantes, France)​​​‌

8.3.1 A​​​‌ Knowledge Graph and Topological​ Data Analysis Framework to​‌ Disentangle the Tomato-Multi Pathogens​​ Complex Gene Regulatory Network​​​‌

Participant: Mathieu Carrière.​

In collaboration with Maxime​‌ Multari, Xavier Amorós-Gabarrón, Alexina​​ Damy, Stéphanie Jaubert, Silvia​​​‌ Bottini (INRAE, France), Sebastian​ Lobentanzer, Julio Saez-Rodriguez and​‌ Aurélien Dugourd (Heidelberg University,​​ Germany)

Global population is​​​‌ rapidly increasing, representing a​ major challenge for food​‌ supply, exacerbated by climate​​ change and environmental degradation.​​​‌ Despite the pivotal role​ of agriculture, plant health​‌ and survival are threatened​​ by various biotic stressors.​​​‌ Although how plants respond​ to each of these​‌ individual stresses is well​​ studied, little is known​​​‌ about how they respond​ to a combination of​‌ many of these bio-aggressors​​ occurring together. To tackle​​​‌ this question, first, we​ built TomTom, a knowledge​‌ graph gathering molecular interactions​​ from nine publicly available​​​‌ databases, including transcription factors-​ or microRNAs- targets, proteinprotein​‌ interactions, and functional terms.​​ Then, we selected transcriptomics​​​‌ data of tomato subjected​ to six distinct pathogens​‌ and performed an integrative​​ analysis. We found 5561​​​‌ candidate genes involved in​ the multi-stress response of​‌ tomato. To study how​​ the response is orchestrated,​​​‌ we mapped those genes​ in TomTom and extracted​‌ a comprehensive gene regulatory​​ network (GRN) composed of​​​‌ 71 transcription factors (TF)​ and 1618 target genes.​‌ By estimating the TF​​ activity, we identified 43​​​‌ TFs responding either specifically​ to one or multiple​‌ bio-aggressors. GRN analyses with​​ a topological data analysis​​​‌ approach allowed to identify​ 18 clusters of TFs​‌ with similar properties, yielding​​ four main configurations localized​​​‌ in specific regions of​ the GRN. Finally, we​‌ found four ERF hubs​​ which cooperatively coordinate the​​​‌ tomato response to multiple​ pathogens. Our findings allowed​‌ to study the complex​​ molecular reprogramming in tomato​​​‌ upon interaction with different​ biotic agents, providing tools​‌ scalable to other questions​​ involving tomato molecular interactions​​​‌ and beyond.

8.3.2 Enhancer​ Dynamics and Spatial Organization​‌ Drive Anatomically Restricted Cellular​​ States in the Human​​​‌ Spinal Cord

Participant: Mathieu​ Carrière.

In collaboration​‌ with Elena K. Kandror,​​ Alexis Peterson, Andreas Tjärnberg,​​​‌ Yuchen Xu, Abbas H.​ Rizvi (University of Wisconsin,​‌ USA), Anqi Wang, Jun​​ Hou Fung, William Pangburn,​​​‌ Raul Rabadan, Tom Maniatis​ (Columbia University, USA), Jackson​‌ Loper (University of Michigan,​​ USA), Will Liao (NY​​​‌ Genome Center, USA), Krishnaa​ T. Mahbubani and Kourosh​‌ Saeb-Parsy (University of Cambridge,​​ UK)

Here, we report​​​‌ the spatial organization of​ RNA transcription and associated​‌ enhancer dynamics in the​​ human spinal cord at​​ single-cell and single-molecule resolution.​​​‌ We expand traditional multiomic‌ measurements to reveal epigenetically‌​‌ poised and bivalent active​​ transcriptional enhancer states that​​​‌ define cell type specification.‌ Simultaneous detection of chromatin‌​‌ accessibility and histone modifications​​ in spinal cord nuclei​​​‌ reveals previously unobserved cell-type‌ specific cryptic enhancer activity,‌​‌ in which transcriptional activation​​ is uncoupled from chromatin​​​‌ accessibility. Such cryptic enhancers‌ define both stable cell‌​‌ type identity and transitions​​ between cells undergoing differentiation.​​​‌ We also define glial‌ cell gene regulatory networks‌​‌ that reorganize along the​​ rostrocaudal axis, revealing anatomical​​​‌ differences in gene regulation.‌ Finally, we identify the‌​‌ spatial organization of cells​​ into distinct cellular organizations​​​‌ and address the functional‌ significance of this observation‌​‌ in the context of​​ paracrine signaling. We conclude​​​‌ that cellular diversity is‌ best captured through the‌​‌ lens of enhancer state​​ and intercellular interactions that​​​‌ drive transitions in cellular‌ state. This study provides‌​‌ fundamental insights into the​​ cellular organization of the​​​‌ healthy human spinal cord.‌

8.3.3 Fermat Distance-to-Measure: a‌​‌ robust Fermat-like metric

Participant:​​ Frédéric Chazal, Jérôme​​​‌ Taupin.

Given a‌ probability measure with density,‌​‌ Fermat distances and density-driven​​ metrics are conformal transformation​​​‌ of the Euclidean metric‌ that shrink distances in‌​‌ high density areas and​​ enlarge distances in low​​​‌ density areas. Although they‌ have been widely studied‌​‌ and have shown to​​ be useful in various​​​‌ machine learning tasks, they‌ are limited to measures‌​‌ with density (with respect​​ to Lebesgue measure, or​​​‌ volume form on manifold).‌ In 45, by‌​‌ replacing the density with​​ the Distance-to-Measure, we introduce​​​‌ a new metric, the‌ Fermat Distance-to-Measure, defined for‌​‌ any probability measure in​​ ${ℝ}^d$. We​​​‌ derive strong stability properties‌ for the Fermat Distance-to-Measure‌​‌ with respect to the​​ measure and propose an​​​‌ estimator from random sampling‌ of the measure, featuring‌​‌ an explicit bound on​​ its convergence speed.

8.4.1 Curvature-Guided Optimal‌ Transport for Rigid Point‌​‌ Cloud Registration

Participant: Mathijs​​ Wintraecken.

In collaboration​​​‌ with Roberto M Dyke‌ (TITANE), Marie-Aurélie Chanut (Cerema‌​‌ - Centre d'Etudes et​​ d'Expertise sur les Risques,​​​‌ l'Environnement, la Mobilité et‌ l'Aménagement), Pierre Alliez (TITANE)‌​‌

The rigid registration of​​ pairs of point sets​​​‌ is a fundamental step‌ for many downstream tasks‌​‌ including shape analysis, reconstruction​​ and localization. There has​​​‌ been a growing interest‌ in the use of‌​‌ Optimal Transport (OT) for​​ point cloud registration problems.​​​‌ However, these techniques face‌ limited adoption due to‌​‌ scalability issues—rendering them impractical—and​​ their sensitivity to missing​​​‌ data commonly encountered in‌ real-world scans. We consider‌​‌ how geometric information may​​ be incorporated into an​​​‌ OT registration framework for‌ improved accuracy and scalability.‌​‌ In this work, we​​ guide mini-batch selection by​​​‌ binning shape features based‌ on local curvature estimates.‌​‌ We demonstrate that our​​ method achieves better results​​​‌ than other OT-based methods‌ and is comparable to‌​‌ the state-of-the-art in terms​​ of successful registrations.

8.4.2​​​‌ Supervised Contamination Detection, with‌ Flow Cytometry Application

Participant:‌​‌ Gilles Blanchard, Frédéric​​ Chazal, Solenne Gaucher​​​‌.

In 15,‌ The contamination detection problem‌​‌ aims to determine whether​​​‌ a set of observations​ has been contaminated, i.e.​‌ whether it contains points​​ drawn from a distribution​​​‌ different from the reference​ distribution. Here, we consider​‌ a supervised problem, where​​ labeled samples drawn from​​​‌ both the reference distribution​ and the contamination distribution​‌ are available at training​​ time. This problem is​​​‌ motivated by the detection​ of rare cells in​‌ flow cytometry. Compared to​​ novelty detection problems or​​​‌ two-sample testing, where only​ samples from the reference​‌ distribution are available, the​​ challenge lies in efficiently​​​‌ leveraging the observations from​ the contamination detection to​‌ design more powerful tests.​​ In this article, we​​​‌ introduce a test for​ the supervised contamination detection​‌ problem. We provide non-asymptotic​​ guarantees on its Type​​​‌ I error, and characterize​ its detection rate. The​‌ test relies on estimating​​ reference and contamination densities​​​‌ using histograms, and its​ power depends strongly on​‌ the choice of the​​ corresponding partition. We present​​​‌ an algorithm for judiciously​ choosing the partition that​‌ results in a powerful​​ test. Simulations illustrate the​​​‌ good empirical performances of​ our partition selection algorithm​‌ and the efficiency of​​ our test. Finally, we​​​‌ showcase our method and​ apply it to a​‌ real flow cytometry dataset.​​

8.4.3 Transductive Conformal Inference​​​‌ for Full Ranking

Participant:​ Gilles Blanchard.

In​‌ collaboration with J-B. Fermanian​​ (U. Montpellier, IMAG, and​​​‌ Inria team IROKO), and​ P. Humbert (CNRS and​‌ Sorbonne Université)

8.4.4 Supervised aggregation​​​‌ of anomaly score functions​ for active anomaly detection​‌

Participant: Martin Royer.​​

In collaboration with Kevin​​​‌ Bleakley (Inria Celest), Mouhcine​ Mendil (IRT Saint Exupéry),​‌ Benjamin Auder (Laboratoire de​​ Mathématiques d'Orsay).

Detecting rare​​​‌ anomalies in batches of​ multidimensional data is challenging.​‌ In 11, we​​ propose a supervised active-learning​​ framework that sends a​​​‌ small number of data‌ points from each batch‌​‌ to an expert for​​ labeling as 'anomaly' or​​​‌ 'nominal', via two mechanisms:‌ (i) points most likely‌​‌ to be an anomaly​​ in the eyes of​​​‌ a supervised classifier trained‌ on previously-labeled data; and‌​‌ (ii) points suggested by​​ an active learner. Instead​​​‌ of, however, training the‌ supervised classifier directly on‌​‌ the current set of​​ labeled raw data points,​​​‌ we treat the scores‌ calculated by an ensemble‌​‌ of M unsupervised anomaly​​ detectors on each data​​​‌ point as if they‌ were the learner's input‌​‌ features. This approach generalizes​​ earlier attempts to linearly​​​‌ aggregate unsupervised anomaly detector‌ scores, and broadens the‌​‌ scope of such methods​​ to ordered data like​​​‌ time series. Results suggest‌ that this method usually‌​‌ outperforms-often significantly-linear strategies. The​​ Python library acanag provides​​​‌ an implementation of the‌ proposed method.

8.4.5 Curvature‌​‌ penalization of strongly anisotropic​​ interfaces models and their​​​‌ phase-field approximation

Participant: Blanche‌ Buet.

In collaboration‌​‌ with Jean-François Babadjian (LMO,​​ Université Paris-Saclay) and Michael​​​‌ Goldman (CMAP, Ecole Polytechnique).‌

25 studies the effect‌​‌ of anisotropy on sharp​​ or diffuse interfaces models.​​​‌ When the surface tension‌ is a convex function‌​‌ of the normal to​​ the interface, the anisotropy​​​‌ is said to be‌ weak. This usually ensures‌​‌ the lower semicontinuity of​​ the associated energy. If,​​​‌ however, the surface tension‌ depends on the normal‌​‌ in a nonconvex way,​​ this so-called strong anisotropy​​​‌ may lead to instabilities‌ related to the lack‌​‌ of lower semicontinuity of​​ the functional. We investigate​​​‌ the regularizing effects of‌ adding a higher order‌​‌ term of Willmore type​​ to the energy. We​​​‌ consider two types of‌ problems. The first one‌​‌ is an anisotropic nonconvex​​ generalization of the perimeter,​​​‌ and the second one‌ is an anisotropic nonconvex‌​‌ Mumford-Shah functional. In both​​ cases, lower semicontinuity properties​​​‌ of the energies with‌ respect to a natural‌​‌ mode of convergence are​​ established, as well as​​​‌ Γ-convergence type results by‌ means of a phase‌​‌ field approximation. In comparison​​ with related results for​​​‌ curvature dependent energies, one‌ of the original aspects‌​‌ of our work is​​ that, in the context​​​‌ of free discontinuity problems,‌ we are able to‌​‌ consider singular structures such​​ as crack-tips or multiple​​​‌ junctions.

8.4.6 Approximate mean‌ curvature flows of a‌​‌ general varifold, and their​​ limit spacetime Brakke flow​​​‌

Participant: Blanche Buet.‌

In collaboration with Gian‌​‌ Paolo Leonardi (University of​​ Trento), Simon Masnou (Université​​​‌ Lyon 1) and Abdelmouksit‌ Sagueni.

In 28,‌​‌ we propose a construction​​ of mean curvature flows​​​‌ by approximation for very‌ general initial data, in‌​‌ the spirit of the​​ works of Brakke and​​​‌ of Kim & Tonegawa‌ based on the theory‌​‌ of varifolds. Given a​​ general varifold, we construct​​​‌ by iterated push-forwards an‌ approximate time-discrete mean curvature‌​‌ flow depending on both​​ a given time step​​​‌ and an approximation parameter.‌ We show that, as‌​‌ the time step tends​​ to 0, this time-discrete​​​‌ flow converges to a‌ unique limit flow, which‌​‌ we call the approximate​​​‌ mean curvature flow. An​ interesting feature of our​‌ approach is its generality,​​ as it provides an​​​‌ approximate notion of mean​ curvature flow for very​‌ general structures of any​​ dimension and codimension, ranging​​​‌ from continuous surfaces to​ discrete point clouds. We​‌ prove that our approximate​​ mean curvature flow satisfies​​​‌ several properties: stability, uniqueness,​ Brakke-type equality, mass decay.​‌ By coupling this approximate​​ flow with the canonical​​​‌ time measure, we prove​ convergence, as the approximation​‌ parameter tends to 0,​​ to a spacetime limit​​​‌ measure whose generalized mean​ curvature is bounded. Under​‌ an additional rectifiability assumption,​​ we further prove that​​​‌ this limit measure is​ a spacetime Brakke flow.​‌

8.4.7 Théorie de l'homotopie​​ quantitative

Participant: Pierre Pansu​​​‌.

Le but de​ la théorie de l'homotopie,​‌ en topologie, c'est de​​ simplifier, après déformation continue,​​​‌ des applications continues entre​ espaces topologiques. Ce qui​‌ empêche de le faire,​​ ce sont des invariants​​​‌ homotopiques. Cela soulève des​ questions quantitatives : -​‌ Le calcul des invariants​​ est-il possible (décidable) ?​​​‌ Si oui, à quel​ coût ? - Construire​‌ des représentants de faible​​ complexité et dont les​​​‌ valeurs des invariants sont​ prescrites est-il possible ?​‌ Si oui, à quel​​ coût ? - Quelle​​​‌ est la complexité des​ déformations nécessaires ? Les​‌ réponses, souvent récentes, sont​​ d'une grande diversité. En​​​‌ outre, bien des questions​ restent ouvertes, montrant que​‌ la topologie n'a pas​​ dit son dernier mot,​​​‌ même en basses dimensions.​

10.1.1 Associate Teams in​​​‌ the framework of an​ Inria International Lab or​‌ in the framework of​​ an Inria International Program​​​‌

10.1.2 Participation in other​‌ International Programs

10.2.1 Visits of​​ international scientists

• Wolfgang Polonik​​​‌ (UC Davis). September-October 2025‌ (1 month).
• Marzieh Eidi‌​‌ (MPI MiS) April-May 2025​​ (2 months).

Extended visit

Participants:‌ Corentin Lunel, Clément‌​‌ Maria.

- Duration​​ : 2024-2025

- Coordinator​​​‌ : Clément Maria

-‌ Location : Institut Montpelliérain‌​‌ Alexandre Grothendieck (IMAG) -​​ Université de Montpellier

The​​​‌ visit consists of federating‌ mathematicians from IMAG working‌​‌ on low dimensional and​​ quantum topology together with​​​‌ computer scientists from Datashape,‌ to work at the‌​‌ interface of the two​​ fields.

10.3.1 ANR

10.3.2​​​‌ Collaboration with other national‌ research institutes

11.1.1 Scientific‌ events: organisation

• Clément Maria‌​‌ was co-organizer of the​​ QuantAzur Days, Nice, November​​​‌ 2025.
• Nina Otter was‌ co-organiser of the conference‌​‌ “Topological methods for time-varying​​ data: theory and applications​​​‌ (TopTime)”, at the Australian‌ National University, Canberra, Australia,‌​‌ November 2025.
• Nina Otter​​ was co-organiser of the​​​‌ workshop “Higher-order interactions at‌ the crossroads of geometry‌​‌ and topology”, Laboratoire de​​ Mathématiques d'Orsay, December 2025.​​​‌

11.1.2 Scientific events: selection‌

11.1.3 Journal

11.1.4 Leadership within​​ the scientific community

• Frédéric​​​‌ Chazal is a member‌ of the Scientific Advisory‌​‌ Board of the Centre​​ for Topological Data Analysis​​​‌ of the Mathematical Institute‌ at Oxford.
• Frédéric Chazal‌​‌ is a member of​​ the Scientific Council of​​​‌ EMAp (ESCOLA DE MATEMÁTICA‌ APLICADA DA FUNDAÇÃO GETULIO‌​‌ VARGAS), Rio de Janeiro,​​ Brasil.
• Mathieu Carrière is​​​‌ a chair holder of‌ the 3IA Institute at‌​‌ Université Côte d'Azur.

11.1.5​​ Scientific expertise

• Frédéric Chazal​​​‌ is a member of‌ the “commission prospective de‌​‌ l’I2M” (Institut de Mathématiques​​ de Marseille).
• Clément Maria​​​‌ was a jury member‌ for the UCA-DS4H PhD‌​‌ grant allocation scheme for​​ 2025.
• Nina Otter is​​​‌ member of the executive‌ committee of the DataIA‌​‌ institute.

11.1.6 Research administration​​

• Marc Glisse is president​​​‌ of the CDT at‌ Inria Saclay.
• Frédéric Chazal‌​‌ is co-responsible of the​​ “programme Mathématiques et IA”​​​‌ of the Fondation Mathématique‌ Jacques Hadamard, Paris-Saclay University‌​‌ (until Oct. 2025).
• Frédéric​​​‌ Chazal is a member​ of the council of​‌ the Graduate School in​​ Mathematics, Paris-Saclay Univ.
• Clément​​​‌ Maria is co-responsible of​ the CNRS-Groupe de Travail​‌ GeoAlgo.
• Clément Maria is​​ a member of the​​​‌ steering committee of the​ QuantAzur federative institute.

11.2.1 Teaching​

• Master: Mathijs Wintraecken, Introduction​‌ to Scientific Research, 2h​​ eq-TD, mineure DS4H (Master​​​‌ and PhD)
• Master: Frédéric​ Chazal, Analyse Topologique des​‌ Données, 30h eq-TD, Université​​ Paris-Saclay, France.
• Master: Frédéric​​​‌ Chazal and Julien Tierny,​ Topological Data Analysis, 38h​‌ eq-TD, M2, Mathématiques, Vision,​​ Apprentissage (MVA), ENS Paris-Saclay,​​​‌ France.
• Master: Mathieu Carrière,​ Basic Algebra for Data​‌ Analysis, 18h eq-TD, MSc​​ DSAI, Université Côte d'Azur​​​‌
• Master: Mathieu Carrière and​ Frédéric Cazals, Geometric and​‌ Topological Methods in Data​​ Analysis, with Applications in​​​‌ Biology and Medecine ,​ 15h eq-TD, MSc DSAI,​‌ Université Côte d'Azur
• Master:​​ Mathieu Carrière, Statistical Learning​​​‌ Theory, 15h eq-TD, MSc​ DSAI, Université Côte d'Azur​‌
• PSL doctoral course: Eddie​​ Aamari, Frédéric Chazal, Alejandro​​​‌ Saldarriaga, 1 week, Topological​ Data Analysis.
• Mini-course at​‌ Young Topologists Meeting 2025​​ : Frédéric Chazal, Persistent​​​‌ homology for machine Learning​ : a measure perspective,​‌ 6h, KTH Stockholm.
• Master:​​ Marc Glisse, Conception et​​​‌ analyse d'algorithmes, 44h eq-TD,​ M1, École Polytechnique, France.​‌

11.2.2 Supervision

• PhD in​​ progress: Rohit Roy. Triangulating​​​‌ stratified spaces. Started on​ November 2025. Mathijs Wintraecken​‌ and Pierre Alliez (TITANE).​​
• PhD in progress: Myriam​​​‌ Frikha, Domain adaptation for​ temporal data. Started in​‌ Nov. 2024. Frédéric Chazal.​​
• PhD in progress: Jérôme​​​‌ Taupin, Density-based metric learning​ and applications in Topological​‌ Data Analysis. Started in​​ Sept. 2025. Frédéric Chazal.​​​‌
• PhD in progress: Anna​ Hollands, Persistent path-homology for​‌ directed-graph analysis: Statistical aspects​​ and applications to machine​​​‌ learning. Started in Oct.​ 2025. Frédéric Chazal and​‌ Bertrand Michel.
• PhD in​​ progress: Alejandro Saldarriaga, Topological​​​‌ Deep Learning. Started in​ Nov. 2025. Eddie Aamari​‌ (ENS Paris) and Frédéric​​ Chazal.
• PhD in progress:​​​‌ Henrique Ennes, Topological approach​ to quantum complexity. Started​‌ in Oct. 2023. Clément​​ Maria and Nicolas Nisse​​​‌ (Inria).
• PhD in progress:​ António Leitao, Persistent homology​‌ of cover refinements and​​ applications to XAI. Started​​​‌ November 2024. Nina Otter​ and Fosca Giannotti (Scuola​‌ Normale Superiore di Pisa)​​

11.2.3 Juries

• Marc Glisse​​​‌ was the external reviewer​ for the PhD defense​‌ of Dominic Desjardins Côté,​​ Université de Sherbrooke, Canada.​​​‌
• Blanche Buet was a​ member of the PhD​‌ Defense jury of Rémi​​ Mougenot (12/2025), Université de​​​‌ Lorraine.
• Mathieu Carrière was​ a member of the​‌ PhD Defense of Mohamed​​ Kissi (10/2025), Université Paris-Sorbonne,​​​‌ and Rayna Andreeva (05/2025),​ University of Edinburgh.
• Nina​‌ Otter was a member​​ of the PhD Defense​​​‌ of Andreas Abildtrup Hansen​ (09/2025), The Technical University​‌ of Denmark.

11.2.4 Productions​​ (articles, videos, podcasts, serious​​​‌ games, ...)

• Clément Maria​ : portrait de chercheur,​‌ exposition Street Science à​​ Nice.
• Clément Maria :​​​‌ Article Mapping the algorithmic​ complexity of topological quantum​‌ computing dans le magazine​​ de l’IdEx d’Université Côte​​​‌ d’Azur INSIGHTS.

11.2.5 Participation​ in Live events

• Blanche​‌ Buet participated in Fête​​ de la Science (at​​ IMO, 10/2025) and in​​​‌ RJMI (at Ens Paris‌ Saclay, 11/2025). Blanche Buet‌​‌ gave a popularization seminar​​ to L3 students (at​​​‌ IMO, 12/2025). Blanche Buet‌ is part of the‌​‌ organizing committee of the​​ FMJH Welcome days for​​​‌ masters (at IMO, 09/2025).‌

11.2.6 Others science outreach‌​‌ relevant activities

• Frédéric Chazal​​ gave a general audience​​​‌ introductory presentation on Artificial‌ Intelligence at Université pour‌​‌ Tous de Bourgogne (March​​ 2025).
• Frédéric Chazal participated​​​‌ in round tables and‌ gave talks on different‌​‌ aspects of AI at​​ the Academie du Renseignement.​​​‌

International‌​‌ journals

• 10 articleL.​​Louis Abraham, C.​​​‌Charles Arnal and A.‌Antoine Marie. Prompt‌​‌ selection matters: enhancing text​​ annotations for social sciences​​​‌ with large language models‌.Journal of Computational‌​‌ Social Science873​​​‌July 2025HALDOI​
• 11 articleK.Kevin​‌ Bleakley, M.Mouhcine​​ Mendil, M.Martin​​​‌ Royer and B.Benjamin​ Auder. Supervised aggregation​‌ of anomaly score functions​​ for active anomaly detection​​​‌.Transactions on Machine​ Learning Research Journal2026​‌. In press. HAL​​back to text
• 12​​​‌ articleE. W.Erin​ Wolf Chambers, C.​‌Christopher Fillmore, E.​​Elizabeth Stephenson and M.​​​‌Mathijs Wintraecken. Burning​ or Collapsing the Medial​‌ Axis is Unstable.​​La MatematicaAugust 2025​​​‌HALDOIback to​ text
• 13 articleE.​‌Erin Chambers, T.​​Tao Ju, D.​​​‌David Letscher, H.​Hannah Schreiber and D.​‌Dan Zeng. VHS:​​ A package for homological​​​‌ simplification of voxelized plant​ root data for skeletonization​‌.Computational Geometry130​​May 2025, 102198​​​‌HALDOI
• 14 article​H.Hana Dal Poz​‌ Kouřimská, A.André​​ Lieutier and M.Mathijs​​​‌ Wintraecken. The medial​ axis of any closed​‌ bounded set is locally​​ Lipschitz stable with respect​​​‌ to the Hausdorff distance​ under ambient diffeomorphisms.​‌Journal of Applied and​​ Computational Topology93​​​‌July 2025, 20​HALDOI
• 15 article​‌S.Solenne Gaucher,​​ G.Gilles Blanchard and​​​‌ F.Frédéric Chazal.​ Supervised Contamination Detection, with​‌ Flow Cytometry Application.​​Biometrika1124August​​​‌ 2025HALDOIback​ to text
• 16 article​‌D.David Loiseaux,​​ M.Mathieu Carrière and​​​‌ A.Andrew Blumberg.​ Multi-parameter Module Approximation: an​‌ efficient and interpretable invariant​​ for multi-parameter persistence modules​​​‌ with guarantees.Journal​ of Applied and Computational​‌ Topology94October​​ 2025, 26HAL​​​‌DOI
• 17 articleW.​Wojciech Reise, B.​‌Bertrand Michel and F.​​Frédéric Chazal. Topological​​​‌ signatures of periodic-like signals​.Bernoulli313​‌2025, 1955-1990HAL​​

International peer-reviewed conferences

• 18​​​‌ inproceedingsL.Lucas Brifault​, D.David Cohen-Steiner​‌ and M.Mathieu Desbrun​​. Efficient and Scalable​​​‌ Spatial Regularization of Optimal​ Transport.SA Conference​‌ Papers '25: SIGGRAPH Asia​​ 2025 Conference PapersSA​​​‌ Conference Papers '25: SIGGRAPH​ Asia 2025 Conference Papers​‌Hong Kong Hong Kong,​​ ChinaACMDecember 2025​​​‌, 1-10HALDOI​back to text
• 19​‌ inproceedingsF.Francesco Conti​​, G.Gianmarco Lazzini​​​‌, R.Raffaele Gaeta​, L. E.Luca​‌ Emanuele Pollina, A.​​Annalisa Comandatore, N.​​​‌Niccolò Furbetta, L.​Luca Morelli, M.​‌Mario D’acunto, D.​​Davide Moroni and M.​​​‌ A.Maria Antonietta Pascali​. Topological Machine Learning​‌ for Raman Spectroscopy: Perspectives​​ for Pancreatic Diseases.​​​‌AITA 2025 - 18th​ International Workshop on Advanced​‌ Infrared Technology and Applications​​Kobe, JapanSeptember 2025​​​‌HALDOI
• 20 inproceedings​F.Francesco Conti,​‌ D.Davide Moroni and​​ M. A.Maria Antonietta​​​‌ Pascali. Topological Machine​ Learning for Discriminative Spectral​‌ Band Identification in Raman​​ Spectroscopy of Pathological Samples​​​‌.AITA 2025 -​ 18th International Workshop on​‌ Advanced Infrared Technology and​​ ApplicationsKobe, JapanSeptember​​​‌ 2025HALDOI
• 21​ inproceedingsH.Henrique Ennes​‌ and C.Clément Maria​​. Hardness of computation​​ of quantum invariants on​​​‌ 3-manifolds with restricted topology‌.Leibniz International Proceedings‌​‌ in Informatics (LIPIcs), ESA​​ 2025ESA 2025 -​​​‌ European Symposium on Algorithms‌ (part of ALGO 2025)‌​‌351Warsaw, PolandSchloss​​ Dagstuhl – Leibniz-Zentrum für​​​‌ Informatik2025HALDOI‌back to text
• 22‌​‌ inproceedingsJ.-B.Jean-Baptiste Fermanian​​, P.Pierre Humbert​​​‌ and G.Gilles Blanchard‌. Transductive Conformal Inference‌​‌ for Full Ranking.​​NeurIPS 2025, The Thirty-Ninth​​​‌ Annual Conference on Neural‌ Information Processing SystemsSan‌​‌ Diego (CA), United States​​December 2025HALback​​​‌ to text
• 23 inproceedings‌C.Corentin Lunel,‌​‌ A.Arnaud de Mesmay​​ and J.Jonathan Spreer​​​‌. Hard Diagrams of‌ Split Links.Leibniz‌​‌ International Proceedings in Informatics​​ (LIPIcs)41st International Symposium​​​‌ on Computational Geometry (SoCG‌ 2025)Kanazawa, JapanSchloss‌​‌ Dagstuhl – Leibniz-Zentrum für​​ Informatik2025HALDOI​​​‌

Reports & preprints

• 24‌ miscR.Rayna Andreeva‌​‌, H.Haydeé Contreras-Peruyero​​, S.Sanjukta Krishnagopal​​​‌, N.Nina Otter‌, M. A.Maria‌​‌ Antonietta Pascali and E.​​Elizabeth Thompson. Fractal​​​‌ dimensions of complex networks:‌ advocating for a topological‌​‌ approach.2025HAL​​DOI
• 25 miscJ.-F.​​​‌Jean-François Babadjian, B.‌Blanche Buet and M.‌​‌Michael Goldman. Curvature​​ penalization of strongly anisotropic​​​‌ interfaces models and their‌ phase-field approximation.October‌​‌ 2025HALback to​​ text
• 26 miscG.​​​‌Gilles Blanchard, N.‌Nicolas Curien, K.‌​‌Klara Krause and A.​​ G.Alexander G. Reisach​​​‌. A phase transition‌ in Barak-Erdős random graphs‌​‌.December 2025HAL​​
• 27 miscG.Gilles​​​‌ Blanchard, J.-B.Jean-Baptiste‌ Fermanian and H.Hannah‌​‌ Marienwald. Estimation of​​ multiple mean vectors in​​​‌ high dimension.March‌ 2025HAL
• 28 misc‌​‌B.Blanche Buet,​​ G. P.Gian Paolo​​​‌ Leonardi, S.Simon‌ Masnou and A.Abdelmouksit‌​‌ Sagueni. Approximate mean​​ curvature flows of a​​​‌ general varifold, and their‌ limit spacetime Brakke flow‌​‌.October 2025HAL​​back to text
• 29​​​‌ miscJ.Jeremie Capitao-Miniconi‌, É.Élisabeth Gassiat‌​‌ and L.Luc Lehéricy​​. Deconvolution of repeated​​​‌ measurements corrupted by unknown‌ noise.July 2025‌​‌HAL
• 30 miscJ.​​Jeremie Capitao-Miniconi, É.​​​‌Élisabeth Gassiat and L.‌Luc Lehéricy. Support‌​‌ and distribution inference from​​ noisy data.February​​​‌ 2025HAL
• 31 misc‌E. W.Erin Wolf‌​‌ Chambers, C.Christopher​​ Fillmore, E.Elizabeth​​​‌ Stephenson and M.Mathijs‌ Wintraecken. Braiding Vineyards‌​‌.November 2025HAL​​
• 32 miscO.Ondřej​​​‌ Draganov, H.Herbert‌ Edelsbrunner, S.Sophie‌​‌ Rosenmeier and M.Morteza​​ Saghafian. Expected Length​​​‌ of the Euclidean Minimum‌ Spanning Tree and 1-norms‌​‌ of Chromatic Persistence Diagrams​​ in the Plane.​​​‌November 2025HAL
• 33‌ miscM.Marzieh Eidi‌​‌ and N.Nina Otter​​. Geometric characterisation of​​​‌ structural and regular equivalences‌ in undirected (hyper)graphs.‌​‌2025HALback to​​ text
• 34 miscH.​​​‌Henrique Ennes and C.‌Clément Maria. Compressed‌​‌ data structures for Heegaard​​ splittings.July 2025​​​‌HALback to text‌
• 35 miscO.Olympio‌​‌ Hacquard, G.Gilles​​​‌ Blanchard and C.Clément​ Levrard. Statistical learning​‌ on measures: an application​​ to persistence diagrams.​​​‌May 2025HAL
• 36​ miscK.Kristóf Huszár​‌ and C.Clément Maria​​. On Sparse Representations​​​‌ of 3-Manifolds.December​ 2025HALback to​‌ text
• 37 miscE.​​ K.Elena K Kandror​​​‌, A.Anqi Wang​, M.Mathieu Carriere​‌, A.Alexis Peterson​​, W.Will Liao​​​‌, A.Andreas Tjarnberg​, J. H.Jun​‌ Hou Fung, K.​​ T.Krishnaa T Mahbubani​​​‌, J.Jackson Loper​, W.William Pangburn​‌, Y.Yuchen Xu​​, K.Kourosh Saeb-Parsy​​​‌, R.Raul Rabadan​, T.Tom Maniatis​‌ and A. H.Abbas​​ H Rizvi. Enhancer​​​‌ Dynamics and Spatial Organization​ Drive Anatomically Restricted Cellular​‌ States in the Human​​ Spinal Cord.January​​​‌ 2025HALDOI
• 38​ miscA.André Lieutier​‌ and M.Mathijs Wintraecken​​. Geodesics of length​​​‌ less than πR in​ a set of reach​‌ R are unique and​​ continuous with respect to​​​‌ the end points.​November 2025HAL
• 39​‌ miscC.Corentin Lunel​​ and C.Clément Maria​​​‌. Well-quasi-orders on embedded​ planar graphs.December​‌ 2025HALback to​​ text
• 40 miscC.​​​‌Clément Maria and H.​Hoel Queffelec. A​‌ fast algorithm for the​​ Hecke representation of the​​​‌ braid group, and applications​ to the computation of​‌ the HOMFLY-PT polynomial and​​ the search for interesting​​​‌ braids.December 2025​HALback to text​‌
• 41 miscL.Lorenzo​​ Mario Amorosa, F.​​​‌Francesco Conti, N.​Nicola Quercioli, F.​‌Flavio Zabini, T.​​ L.Tayebeh Lotfi Mahyari​​​‌, Y.Yiqun Ge​ and P.Patrizio Frosini​‌. Reconstruction of SINR​​ Maps from Sparse Measurements​​​‌ using Group Equivariant Non-Expansive​ Operators.October 2025​‌HAL
• 42 miscM.​​Maxime Multari, M.​​​‌Mathieu Carriere, X.​Xavier Amoros-Gabarron, A.​‌Alexina Damy, S.​​Sebastien Lobentanzer, J.​​​‌Julio Saez-Rodriguez, S.​Stephanie Jaubert, A.​‌Aurelien Dugourd and S.​​Silvia Bottini. A​​​‌ knowledge graph and topological​ data analysis framework to​‌ disentangle the tomato-multi pathogens​​ complex gene regulatory network​​​‌.April 2025HAL​
• 43 miscZ.Ziyad​‌ Oulhaj, M.Mathieu​​ Carrière and B.Bertrand​​​‌ Michel. Gromov-Wasserstein Bound​ between Reeb and Mapper​‌ Graphs.2025HAL​​
• 44 miscP.Pierre​​​‌ Pansu. Théorie de​ l'homotopie quantitative: d'après Guth,​‌ Manin, Weinberger,....January​​ 2025HAL
• 45 misc​​​‌J.Jérôme Taupin and​ F.Frédéric Chazal.​‌ Fermat Distance-to-Measure: a robust​​ Fermat-like metric.April​​​‌ 2025HALback to​ text

Other scientific publications​‌

• 46 inproceedingsR. M.​​Roberto M Dyke,​​​‌ M.Mathijs Wintraecken,​ M.-A.Marie-Aurélie Chanut and​‌ P.Pierre Alliez.​​ Curvature-Guided Optimal Transport for​​​‌ Rigid Point Cloud Registration​.SGP 2025 -​‌ Symposium on Geometry Processing​​Bilbao, SpainJuly 2025​​​‌HAL