3.2.1 Reconstruction by Data Integration

Large protein assemblies such as the Nuclear Pore Complex (NPC), chaperonin cavities, the proteasome or ATP synthases, to name a few, are key to numerous biological functions. To improve our understanding of these functions, one would ideally like to build and animate atomic models of these molecular machines. However, this task is especially tough, due to their size and their plasticity, but also due to the flexibility of the proteins involved. In a sense, the modeling challenges arising in this context are different from those faced for binary docking, and also from those encountered for intermediate size complexes which are often amenable to a processing mixing (cryo-EM) image analysis and classical docking. To face these new challenges, an emerging paradigm is that of reconstruction by data integration 27. In a nutshell, the strategy is reminiscent from NMR and consists of mixing experimental data from a variety of sources, so as to find out the model(s) best complying with the data. This strategy has been in particular used to propose plausible models of the Nuclear Pore Complex 26, the largest assembly known to date in the eukaryotic cell, and consisting of 456 protein instances of 30 types.

3.2.2 Modeling with Uncertainties and Model Assessment

Reconstruction by data integration requires three ingredients. First, a parametrized model must be adopted, typically a collection of balls to model a protein with pseudo-atoms. Second, as in NMR, a functional measuring the agreement between a model and the data must be chosen. In 25, this functional is based upon restraints, namely penalties associated to the experimental data. Third, an optimization scheme must be selected. The design of restraints is notoriously challenging, due to the ambiguous nature and/or the noise level of the data. For example, Tandem Affinity Purification (TAP) gives access to a pullout i.e. a list of protein types which are known to interact with one tagged protein type, but no information on the number of complexes or on the stoichiometry of proteins types within a complex is provided. In cryo-EM, the envelope enclosing an assembly is often imprecisely defined, in particular in regions of low density. For immuno-EM labelling experiments, positional uncertainties arise from the microscope resolution.

These uncertainties coupled with the complexity of the functional being optimized, which in general is non convex, have two consequences. First, it is impossible to single out a unique reconstruction, and a set of plausible reconstructions must be considered. As an example, 1000 plausible models of the NPC were reported in 25. Interestingly, averaging the positions of all balls of a particular protein type across these models resulted in 30 so-called probability density maps, each such map encoding the probability of presence of a particular protein type at a particular location in the NPC. Second, the assessment of all models (individual and averaged) is non trivial. In particular, the lack of straightforward statistical analysis of the individual models and the absence of assessment for the averaged models are detrimental to the mechanistic exploitation of the reconstruction results. At this stage, such models therefore remain qualitative.

Modeling Interfaces and Contacts

In modeling interfaces and contacts, one may favor geometric or topological information.

On the geometric side, the problem of modeling contacts at the atomic level is tantamount to encoding multi-body relations between an atom and its neighbors. On the one hand, one may use an encoding of neighborhoods based on geometric constructions such as Voronoi diagrams (affine or curved) or arrangements of balls. On the other hand, one may resort to clustering strategies in higher dimensional spaces, as the $p$ neighbors of a given atom are represented by $3p-6$ degrees of freedom – the neighborhood being invariant upon rigid motions. The information gathered while modeling contacts can further be integrated into interface models.

On the topological side, one may favor constructions which remain stable if each atom in a structure retains the same neighbors, even though the 3D positions of these neighbors change to some extent. This process is observed in flexible docking cases, and call for the development of methods to encode and compare shapes undergoing tame geometric deformations.

Modeling Macro-molecular Assemblies

In dealing with large assemblies, a number of methodological developments are called for.

On the experimental side, of particular interest is the disambiguation of proteomics signals. For example, TAP and mass spectrometry data call for the development of combinatorial algorithms aiming at unraveling pairwise contacts between proteins within an assembly. Likewise, density maps coming from electron microscopy, which are often of intermediate resolution (5-10Å) call the development of noise resilient segmentation and interpretation algorithms. The results produced by such algorithms can further be used to guide the docking of high resolutions crystal structures into maps.

As for modeling, two classes of developments are particularly stimulating. The first one is concerned with the design of algorithms performing reconstruction by data integration, a process reminiscent from non convex optimization. The second one encompasses assessment methods, in order to single out the reconstructions which best comply with the experimental data. For that endeavor, the development of geometric and topological models accommodating uncertainties is particularly important.

Modeling the Flexibility of Macro-molecules

Given a sampling on an energy landscape, a number of fundamental issues actually arise: how does the point cloud describe the topography of the energy landscape (a question reminiscent from Morse theory)? Can one infer the effective number of degrees of freedom of the system over the simulation, and is this number varying? Answers to these questions would be of major interest to refine our understanding of folding and docking, with applications to the prediction of structural properties. It should be noted in passing that such questions are probably related to modeling phase transitions in statistical physics where geometric and topological methods are being used 41.

From an algorithmic standpoint, such questions are reminiscent of shape learning. Given a collection of samples on an (unknown) model, learning consists of guessing the model from the samples – the result of this process may be called the reconstruction. In doing so, two types of guarantees are sought: topologically speaking, the reconstruction and the model should (ideally!) be isotopic; geometrically speaking, their Hausdorff distance should be small. Motivated by applications in Computer Aided Geometric Design, surface reconstruction triggered a major activity in the Computational Geometry community over the past ten years. Aside from applications, reconstruction raises a number of deep issues: the study of distance functions to the model and to the samples, and their comparison; the study of Morse-like constructions stemming from distance functions to points; the analysis of topological invariants of the model and the samples, and their comparison.

6.1.1 SBL

• Name: Structural Bioinformatics Library
• Keywords: Structural Biology, Biophysics, Software architecture
• Functional Description:

  The SBL is a generic C++/python cross-platform software library targeting complex problems in structural bioinformatics. Its tenet is based on a modular design offering a rich and versatile framework allowing the development of novel applications requiring well specified complex operations, without compromising robustness and performances.

  More specifically, the SBL involves four software components (1-4 thereafter). For end-users, the SBL provides ready to use, state-of-the-art (1) applications to handle molecular models defined by unions of balls, to deal with molecular flexibility, to model macro-molecular assemblies. These applications can also be combined to tackle integrated analysis problems. For developers, the SBL provides a broad C++ toolbox with modular design, involving core (2) algorithms, (3) biophysical models, and (4) modules, the latter being especially suited to develop novel applications. The SBL comes with a thorough documentation consisting of user and reference manuals, and a bugzilla platform to handle community feedback.

• Release Contributions: In 2020, four new packages have been released. Two of them belong to the Applications group: molecular cradle, to study the relative motions of subunits in large molecular machines, and multiple interface string alignments, to compare the interfaces of protein complexes involving similar molecules. Two of them belong to the core of the library: Wang-Landau proposes a generic implementation of the eponym algorithm, while Hamiltonian Monte Carlo (HMC) makes available a robust implementation of HMC, with applications to the computation of the volume of high dimensional polytopes.
• URL: https://sbl.inria.fr/
• Publication: hal-01570848
• Contact: Frédéric Cazals

7.1.1 Comparing interfaces in protein complexes

Participant: F. Cazals.

In collaboration with S. Bereux (Ecole Polytechnique), and B. Delmas (INRAe, Jouy-en-Josas).

We introduce Multiple Interface String Alignment (MISA) 20, a visualization tool to display coherently various sequence and structure based statistics at protein-protein interfaces (SSE elements, buried surface area, $\Delta ASA$, B factor values, etc). The amino-acids supporting these annotations are obtained from Voronoi interface models. The benefit of MISA is to collate annotated sequences of (homologous) chains found in different biological contexts i.e.bound with different partners or unbound. The aggregated views MISA/SSE, MISA/BSA, MISA/$\Delta ASA$ etc make it trivial to identify commonalities and differences between chains, to infer key interface residues, and to understand where conformational changes occur upon binding. As such, they should prove of key relevance for knowledge based annotations of protein databases such as the Protein Data Bank.

Illustrations are provided on the receptor binding domain (RBD) of coronaviruses, in complex with their cognate partner or (neutralizing) antibodies. MISA computed with a minimal number of structures complement and enrich findings previously reported.

The corresponding package is available from the Structural Bioinformatics Library (https://sbl.inria.fr

and https://sbl.inria.fr/doc/Multiple_interface_string_alignment-user-manual.html).

7.1.2 Modeling the efflux mechanism of AcrB

Participant: F. Cazals, M. Simsir.

In collaboration with I. Broutin (Univ. Paris Descartes and CNRS), and I. Mus-Veteau (Université Côte d'Azur and IPMC/CNRS).

RND family proteins are transmembrane proteins identified as large spectrum drug transporters involved in multi-drug resistance. A prototypical case in this superfamily, responsible for antibiotic resistance in selected gram negative bacteria, is AcrB. AcrB forms a trimer using the proton motive force to efflux drugs, implementing a functional rotation mechanism. Unfortunately, the size of the system (1049 amino-acid per monomer and membrane) has prevented a systematic dynamical exploration, so that the mild understanding of this coupled transport jeopardizes our ability to counter it.

The large number of crystal structures of AcrB prompts studies to further our understanding of the mechanism. To this end, we present 24 a novel strategy based on two key ingredients which are to study dynamics by exploiting information embodied in the numerous crystal structures obtained to date, and to systematically consider subdomains, their dynamics, and their interactions. Along the way, we identify the subdomains responsible for dynamic events, refine the states (A,B,E) of the functional rotation mechanism, and analyze the evolution of intramonomer and intermonomer interfaces along the functional cycle.

Our analysis shows the relevance of AcrB's efflux mechanism as a template within the HAE1 family but not beyond. It also paves the way to targeted simulations exploiting the most relevant degrees of freedom at certain steps, and also to a targeting of specific interfaces to block the drug efflux.

Our work shows that complex dynamics can be unveiled from static snapshots, a strategy that may be used on a variety of molecular machines of large size.

7.2.1 Wang-Landau Algorithm: an adapted random walk to boost convergence

Participant: F. Cazals, A. Chevallier.

The Wang-Landau (WL) algorithm is a recently developed stochastic algorithm computing densities of states of a physical system, and also performing numerical integration in high dimensional spaces. Since its inception, it has been used on a variety of (bio-)physical systems, and in selected cases, its convergence has been proved. The convergence speed of the algorithm is tightly tied to the connectivity properties of the underlying random walk.

In this work 16, we propose an efficient random walk that uses geometrical information to circumvent the following inherent difficulties: avoiding overstepping strata, toning down concentration phenomena in high-dimensional spaces, and accommodating multidimensional distributions. These improvements are especially well suited to improve calculations on a per basin basis – included anharmonic ones.

Experiments on various models stress the importance of these improvements to make WL effective in challenging cases. Altogether, these improvements make it possible to compute density of states for regions of the phase space of small biomolecules.

7.2.2 A generic software framework for Wang-Landau type algorithms

Participant: F. Cazals, A. Chevallier.

The Wang-Landau (WL) algorithm is a stochastic algorithm designed to compute densities of states of a physical system. Is has also been recently used to perform challenging numerical integration in high-dimensional spaces. Using WL requires specifying the system handled, the proposal to explore the definition domain, and the measured against which one integrates. Additionally, several design options related to the learning rate must be provided.

This work 22 presents the first generic (C++) implementation providing all such ingredients. The versatility of the framework is illustrated with a variety of problems including the computation of density of states of physical systems and biomolecules, and the computation of high dimensional integrals. Along the way, we that integrating against a Boltzmann like measure to estimate DoS with respect to the Lebesgue measure can be beneficial.

We anticipate that our implementation, available in the Structural Bioinformatics Library (http://sbl.inria.fr), will leverage experiments on complex systems and contribute to unravel free energy calculations for (bio-)molecular systems.

7.3.1 Fréchet mean and $p$-mean on the unit circle: characterization, decidability, and algorithm

Participant: F. Cazals, T. O'Donnell.

In collaboration with B. Delmas (INRAe, Jouy-en-Josas).

The center of mass of a point set lying on a manifold generalizes the celebrated Euclidean centroid, and is ubiquitous in statistical analysis in non Euclidean spaces. In 21, we give a complete characterization of the weighted $p$-mean of a finite set of angular values on $S^1$, based on a decomposition of $S^1$ such that the functional of interest has at most one local minimum per cell. This characterization is used to show that the problem is decidable for rational angular values –a consequence of Lindemann's theorem on the transcendence of $\pi$, and to develop an effective algorithm parameterized by exact predicates. A robust implementation of this algorithm based on multi-precision interval arithmetic is also presented. This implementation is effective for large values of $n$ and $p$. Experiments on random sets of angles and protein dihedral angles consistently show that the Fréchet mean ($p=2$) yields a variance reduction of $\sim 20\%$ with respect to the classically used circular mean.

Our derivations are of interest in two respects. First, efficient $p$-mean calculations are relevant to develop principal components analysis on the flat torus encoding angular spaces–a particularly important case to describe molecular conformations. Second, our two-stage strategy stresses the interest of combinatorial methods for p-means, also emphasizing the role of numerical issues.

The implementation is available in the Structural Bioinformatics Library (http://sbl.inria.fr).

7.3.2 Improved polytope volume calculations based on Hamiltonian Monte Carlo with boundary reflections and sweet arithmetics

Participant: F. Cazals, A. Chevallier.

In collaboration with S. Pion IMS (Univ. Bordeaux / Bordeaux INP / CNRS UMR 5218).

Computing the volume of a high dimensional polytope is a fundamental problem in geometry, also connected to the calculation of densities of states in statistical physics, and a central building block of such algorithms is the method used to sample a target probability distribution.

The work 23 studies Hamiltonian Monte Carlo (HMC) with reflections on the boundary of a domain, providing an enhanced alternative to Hit-and-run (HAR) to sample a target distribution restricted to the polytope. We make three contributions. First, we provide a convergence bound, paving the way to more precise mixing time analysis. Second, we present a robust implementation based on multi-precision arithmetic – a mandatory ingredient to guarantee exact predicates and robust constructions. We however allow controlled failures to happen, introducing the Sweeten Exact Geometric Computing (SEGC) paradigm. Third, we use our HMC random walk to perform H-polytope volume calculations, using it as an alternative to HAR within the volume algorithm by Cousins and Vempala. The tests, conducted up to dimension 50, show that the HMC random walk outperforms HAR.

7.3.3 Overlaying a hypergraph with a graph with bounded maximum degree, with application for low-resoluton reconstructions of molecular assemblies

Participant: D. Mazauric.

In collaboration with F. Havet (CNRS, I3S, Inria/I3S project-team Coati) V.-H. Nguyen (Inria, Inria/I3S project-team Coati), and R. Watrigant (Univ. Lyon).

In the article 18, we analyze a generalization of the minimum connectivity inference problem (MCI). MCI models the computation of low-resolution structures of macro-molecular assemblies, based on data obtained by native mass spectrometry. The generalization studied in this article, allows us to consider more refined constraints for the characterization of low resolution models of large assemblies. We model this problem by using hypergraphs: for a (possibly infinite) fixed family of graphs $F$, we say that a graph $G$ overlays $F$ on a hypergraph $H$ if $V\left(H\right)$ is equal to $V\left(G\right)$ and the subgraph of $G$ induced by every hyperedge of $H$ contains some member of $F$ as a spanning subgraph. While it is easy to see that the complete graph on $\left|V\right(H\left)\right|$ overlays $F$ on a hypergraph $H$ whenever the problem admits a solution, the Minimum $F$-Overlay problem asks for such a graph with at most $k$ edges, for some given $k\in \mathbb{N}$. This problem allows to generalize some natural problems which may arise in practice. For instance, if the family $F$ contains all connected graphs, then Minimum $F$-Overlay corresponds to the MCI problem.

Let $G$ and $H$ be respectively a graph and a hypergraph defined on a same set of vertices, and let $F$ be a fixed graph. We say that $G$  $F$-overlays a hyperedge $S$ of $H$ if $F$ is a spanning subgraph of the subgraph of $G$ induced by $S$, and that it $F$-overlays $H$ if it $F$-overlays every hyperedge of $H$. In this article, we study the computational complexity of two new problems, taking into account degree constraints (for example a protein cannot have many other proteins in its neighborhoud). The first problem, $(\Delta \le k)$$F$-Overlay, consists in deciding whether there is a graph with maximum degree at most $k$ that $F$-overlays a given hypergraph $H$. It is a particular case of the second problem Max $(\Delta \le k)$$F$-Overlay, which takes a hypergraph $H$ and an integer $s$ as input, and consists in deciding whether there is a graph with maximum degree at most $k$ that $F$-overlays at least $s$ hyperedges of $H$. We give a complete polynomial/NP-complete dichotomy for the Max $(\Delta \le k)$-$F$-Overlay problems depending on the pairs $(F,k)$, and establish the complexity of $(\Delta \le k)$$F$-Overlay for many pairs $(F,k)$.

7.3.4 Sequential metric dimension

Participant: D. Mazauric.

In collaboration with J. Bensmail (I3S, Inria/I3S project-team Coati) and F. Mc Inerney (Inria/I3S project-team Coati) and N. Nisse (Inria, Inria/I3S project-team Coati) and S. Pérennes (CNRS, Inria/I3S project-team Coati).

In the localization game, introduced by Seager in 2013, an invisible and immobile target is hidden at some vertex of a graph $G$. At every step, one vertex $v$ of $G$ can be probed which results in the knowledge of the distance between $v$ and the secret location of the target. The objective of the game is to minimize the number of steps needed to locate the target whatever be its location.

In the article 14, we address the generalization of this game where $k\ge 1$ vertices can be probed at every step. Our game also generalizes the notion of the metric dimension of a graph. Precisely, given a graph $G$ and two integers $k,\ell \ge 1$, the localization problem asks whether there exists a strategy to locate a target hidden in $G$ in at most $\ell$ steps and probing at most $k$ vertices per step. We first show that, in general, this problem is NP-complete for every fixed $k\ge 1$ (resp., $\ell \ge 1$). We then focus on the class of trees. On the negative side, we prove that the localization problem is NP-complete in trees when $k$ and $\ell$ are part of the input. On the positive side, we design a $(+1)$-approximation for the problem in $n$-node trees, i.e., an algorithm that computes in time $O(nlogn)$ (independent of $k$) a strategy to locate the target in at most one more step than an optimal strategy. This algorithm can be used to solve the localization problem in trees in polynomial time if $k$ is fixed. We also consider some of these questions in the context where, upon probing the vertices, the relative distances to the target are retrieved. This variant of the problem generalizes the notion of the centroidal dimension of a graph.

7.3.5 Distributed link scheduling

Participant: D. Mazauric.

In collaboration with J.-C. Bermond (I3S, Inria/I3S project-team Coati), V. Misra (Columbia University), and P. Nain (Inria, Inria project-team Neo).

In the article 15, we investigate distributed transmission scheduling in wireless networks. Due to interference constraints, “neighboring links” cannot be simultaneously activated, otherwise transmissions will fail. Here, we consider any binary model of interference. We use a model described by Bui, Sanghavi, and Srikant. We assume that time is slotted and during each slot there are two phases: one control phase in which a link scheduling algorithm determines a set of non interfering links to be activated, and a data phase in which data is sent through these links. We assume random arrivals on each link during each slot, so that a queue is associated to each link. Since nodes do not have a global knowledge of the queues sizes, our aim is to design a distributed link scheduling algorithm. To be efficient the control phase should be as short as possible; this is done by exchanging control messages during a constant number of mini-slots (constant overhead).

In this paper, we design the first fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues), and it does not require any knowledge of the queue-lengths. We prove that this algorithm gives a maximal set of active links, where for any non-active link there exists at least one active link in its interference set. We also establish sufficient conditions for stability under general Markovian assumptions. Finally, the performance of our algorithm (throughput, stability) is investigated and compared via simulations to that of previously proposed schemes.

9.1.1 Scientific events: organisation

• Frédéric Cazals co-organized the winter school Algorithms in Structural Bioinformatics, Intrinsic Disorder in Protein: From Non-Folding to Fuzzy Recognition to Phase Separation, CNRS center of Cargèse, November 23rd–27th. Unfortunately, the school was canceled due to the pandemics.
• Frédéric Cazals co-organized the Symposium Multidisciplinary approaches in cancer research, Inria Sophia, Nov. 16-17, 2020. Unfortunately, the school was canceled due to the pandemics.

9.1.2 Invited talks

– Frédéric Cazals gave the following invited talks:

• Comparing (interface) models: a multivariate data analysis perspective, Elixir - 3DBioInfo, Cambridge (visio-conference), November 2020.
• Multiple Interface String Alignments: Boosting the analysis of protein interfaces, with applications to the SARS-Cov-2 spike, GDR BIM/GT MASIM, meeting dedicated to SARS-Cov-2, November 2020.
• Clustering algorithms for structural studies: insights on novel metrics and cluster stability assessment, Algorithms for integrative structural biology, Grenoble, March 2020.

9.1.3 Leadership within the scientific community

– Frédéric Cazals:

• 2010-.... Member of the steering committee of the GDR Bioinformatique Moléculaire, for the Structure and macro-molecular interactions theme.
• 2017-.... Co-chair, with Yann Ponty, of the working group / groupe de travail (GT MASIM - Méthodes Algorithmiques pour les Structures et Interactions Macromoléculaires, within the GDR de BIoinformatique Moléculaire (GDR BIM, https://www.gdr-bim.cnrs.fr/).

9.1.4 Scientific expertise

– Frédéric Cazals:

• 2020: member of the IUF senior panel.

9.1.5 Research administration

– Frédéric Cazals:

• 2018-...: Member of the bureau du comité des équipes projets.
• 2020-...: Member of the bureau of the EUR Life, Université Côte d'Azur.

9.2.1 Teaching

• Master: Data Sciences Program, Department of Applied Mathematics, Ecole Centrale-Supélec: Frédéric Cazals (Inria ABS) and Frédéric Chazal (Inria Saclay), Foundations of Geometric Methods in Data Analysis, Web: http://www-sop.inria.fr/abs/teaching/centrale-FGMDA/centrale-FGMDA--cazals-carriere-2020-2021.html
• Master: Frédéric Cazals (Inria ABS), Understanding biomolecular interactions and simulations: a primer in statistical physics for biomolecules, Polytech Nice Sophia, Université Côte d'Azur, Master Bio-informatique.
• Master : Dorian Mazauric, Algorithmique et Complexité, 23h30 TD, niveau M1, Polytech Nice Sophia, Université Côte d'Azur, filière Sciences Informatiques, France.

9.2.2 Supervision

• PhD in progress, 3rd year: Méliné Simsir, Modeling drug efflux by Patched. Université Côte d'Azur. Thesis co-supervised by Frédéric Cazals and Isabelle Mus-Veteau, IPMC/CNRS.
• PhD in progress, 2nd year: Timothée O'Donnel, Modeling the influenza polymerase. Université Côte d'Azur. Thesis co-supervised by Frédéric Cazals and Bernard Delmas, INRAe Jouy-en-Josas.
• PhD in progress, 2nd year : Thi Viet Ha Nguyen, Graph Algorithms techniques for (low and high) resolution models of large protein assemblies, Frédéric Havet (Inria/I3S project-team Coati) and Dorian Mazauric.

9.2.3 Juries

– Frédéric Cazals:

1. Julien Bensmail, Habilitation thesis, Université Côte d'Azur, December 2020. Committee member (president) for the habilitation Contribution aux ponderations distinguantes de graphes.
2. Meline Simsir, PhD thesis, Université Côte d'Azur, December 2020. Committee member (co-supervisor) for the PhD thesis Structural modeling of RND family efflux pumps : from antibio-resistance to chemotherapy resistance
3. Siddarth Pritam, PhD thesis, Université Côte d'Azur, March 2020. Committee member (president) for the thesis Collapses and Persistent Homology.
4. Shard Goulam Abas, PhD thesis, U. Paris-Saclay, April 2020. Rapporteur on the thesis Développement de méthodes mathématiques pour l’analyse de trajectoires conformationnelles en dynamique moléculaire. Advisors: A. Trouvé (U. Paris-Saclay), L. Tchertanov (CNRS).

9.3.1 Internal or external Inria responsibilities

– Dorian Mazauric:

• 2019-.... Head of Commission Mastic (Médiation et Animation des MAthématiques, des Sciences et Techniques Informatiques et des Communications), Inria Sophia Antipolis - Méditerranée.
• 2019-.... Coordinator of Terra Numerica – vers une Cité du Numérique (https://terra-numerica.org), an ambitious scientific popularisation project. Its main goal is to create a "Dedicated Digital space" in the south of France, (in the spirit of the "Cité des Sciences" or "Palais de la découverte" in Paris). To do so, Terra Numerica is developing and structuring popularisation activities, supports which are available at the Maison de l'Intelligence Artificielle and also spread in different antennas throughout the territory (e.g. in schools, exhibition extensions...). This large-scale project involves (brings together) all the actors of research, education, industry, associations and collectivities... It is actually composed of more than one hundred people.
• 2018-.... Member of the Conseil d'Administration de l'association les Petits Débrouillards.
• 2017-.... Member of projet de médiation Galéjade : Graphes et ALgorithmes : Ensemble de Jeux À Destination des Ecoliers... (mais pas que).

9.3.2 Interventions

– Dorian Mazauric:

• 03-04/10/2020 : Ateliers et conférence au village des sciences de Villeneuve-Loubet. Fête de la Science 2020.
• 14/08/2020 : Intervention stages Découverte des métiers du Numérique des Petits Débrouillards. Ariane, Nice.
• 12/02/2020 : Formation d’une centaine d’enseignants de cycle 1 de la circonscription d’Antibes. Algorithmes et graphes.
• 08/02/2020 : Forum des métiers au lycée Hutinel, Cannes-la-Bocca. Organisé par Rotary Club Palm Beach. Présentation des métiers en sciences du numérique.
• 04/02/2020 : Conférence au collège Sydney Bechet, Antibes Juan-les-Pins. Algorithmes.
• 28/01/2020 : Journée de formation organisée par Canopé à Toulon. Thème de la journée : robotique éducative et apprentissages fondamentaux – défis robotiques déclinés pour tous les niveaux, adossés aux apprentissages disciplinaires et transversaux. Graphes, algorithmes et magie des mathématiques et de l’informatique.

International journals

• 14 articleJulienJ. Bensmail, DorianD. Mazauric, FionnF. Mc Inerney, NicolasN. Nisse and StéphaneS. Pérennes. Sequential Metric DimensionAlgorithmica82102020, 2867-2901
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• 15 articleJean-ClaudeJ.-C. Bermond, DorianD. Mazauric, VishalV. Misra and PhilippeP. Nain. Distributed Link Scheduling in Wireless NetworksDiscrete Mathematics, Algorithms and Applications1252020, 1-38
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• 16 articleAugustinA. Chevallier and FrédéricF. Cazals. Wang-Landau Algorithm: an adapted random walk to boost convergenceJournal of Computational Physics4102020, 109366
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• 17 articleViet-HaV.-H. Nguyen, KévinK. Perrot and MathieuM. Vallet. NP-completeness of the game KingdominoTheoretical Computer Science822June 2020, 23-35
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International peer-reviewed conferences

• 18 inproceedings FrédéricF. Havet, DorianD. Mazauric, Viet-HaV.-H. Nguyen and RémiR. Watrigant. Overlaying a hypergraph with a graph with bounded maximum degree CALDAM 2020 - 6th Annual International Conference on Algorithms and Discrete Applied Mathematics Hyderabad, India February 2020
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• 19 inproceedings FrédéricF. Havet, DorianD. Mazauric, Viet-HaV.-H. Nguyen and RémiR. Watrigant. Overlaying a hypergraph with a graph with bounded maximum degree ALGOTEL 2020 – 22èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications Lyon, France September 2020
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Reports & preprints

• 20 misc StéphaneS. Bereux, BernardB. Delmas and FrédéricF. Cazals. Boosting the analysis of protein interfaces with Multiple Interface String Alignment: illustration on the spikes of coronaviruses September 2020
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• 21 misc FrédéricF. Cazals, BernardB. Delmas and TimothéeT. O'donnell. Fréchet mean and p-mean on the unit circle: characterization, decidability, and algorithm February 2020
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• 22 misc AugustinA. Chevallier and FrédéricF. Cazals. A generic software framework for Wang-Landau type algorithms March 2020
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• 23 misc AugustinA. Chevallier, SylvainS. Pion and FrédéricF. Cazals. Improved polytope volume calculations based on Hamiltonian Monte Carlo with boundary reflections and sweet arithmetics December 2020
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• 24 misc MélinéM. Simsir, IsabelleI. Broutin, IsabelleI. Mus-Veteau and FrédéricF. Cazals. Studying dynamics without explicit dynamics: a structure-based study of the export mechanism by AcrB September 2020
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