Applied Mathematics

Picture : morphing based on Riemannian optimization concepts. Click here for details.

The Applied Mathematics group gathers 8 professors and about twenty researchers who are working on several subfields.

Principal Investigators :

Pierre-Antoine AbsilVincent Blondel, Jean-Charles Delvenne, François Glineur, Geovani Grapiglia, Laurent Jacques, Raphaël Jungers, Estelle Massart

Research Lab :

INMA (Mathematical Engineering research division)

Research Areas :

Research in the algebra team focuses on various structures whose automorphism groups are linear algebraic groups, notably quadratic forms and algebras over arbitrary fields. These structures are studied using methods from number theory and algebraic geometry, such as valuation theory and Galois cohomology. The current projects aim at developing new cohomological invariants and a noncommutative valuation theory for central simple algebras with involution. This activity is run in cooperation with the group theory team of the IRMP.

Balance laws are hyperbolic partial differential equations that are commonly used to express the fundamental dynamics of open conservative systems. Many physical systems having an engineering interest are described by systems of one-dimensional hyperbolic balance laws. Typical examples are for instance the telegrapher equations for electrical lines, the shallow water (Saint-Venant) equations for open channels, the Euler equations for gas flow in pipelines or the Aw-Rascle equations for road traffic. In this research, our concern is to analyse the exponential stability (in the sense of Lyapunov) of the steady-states of such systems.

This research relies on the use of non-negative convex algebra for solving underdetermined linear systems of equations under positive constraints. Such problems arise in various domains of Systems Biology. We are particularly concerned with the decomposition of complex metabolic networks into elementary pathways and with the metabolic flux analysis which aims at computing the entire intracellular flux distribution from a limited number of flux measurements.

The group works on numerical methods for rational approximation, linear algebra and optimization with applications in systems and control, economy, biology and medicine. In approximation theory we look at approximation problems in the complex plane (orthogonal polynomials, quadrature formulas) and at the solution of functional equations, with applications in science, technology and economy. In linear algebra we study the model reduction problem via interpolation and projection of state-space models. We also look at optimal Hankel-norm approximations and their formulation via convex optimization techniques.  In optimization, we are looking for general schemes with provable global complexity estimates. This extends onto the methods for solving systems of nonlinear equations and optimization on nonlinear manifolds. These techniques are applied to problems in signals and systems.

We study several types of matrix factorization techniques, in particular variants where nonnegative factors are required. We focus on both algorithmic (mehods and computational complexity) and applicative (machine learning, graph problems, polyhedral combinatorics) points of view.

The complex rheological behaviour of non-Newtonian liquids is dictated by the flow induced evolution of their internal microstructure. For example, in homogeneous polymeric fluids, the relevant microstructure is the conformation of the macromolecules. Each macroscopic fluid element contains a large number of polymers with a statistical distribution of conformations. During flow, the polymer conformations evolve along the fluid trajectories. Also, the macroscopic stress carried by each fluid element is itself governed by the distribution of conformations within that element. One thus faces a highly non-linear coupling between rheological behaviour, flow-induced evolution of the microstructure, and flow conditions. The fundamental scientific challenges in rheology and non-Newtonian fluid mechanics are indeed to fully comprehend the nature of this non-linear coupling and to predict its consequences in flow problems of interest. We currently focus on the development of molecular models of kinetic theory and methods of computational rheology.

Most recent publications

Below are listed the 10 most recent journal articles and conference papers produced in this research area. You also can access all publications by following this link : see all applied mathematics publications.

Journal Articles

1. Stollenwerk, Alexander; Dirksen, Sjoerd; Genzel, Martin; Jacques, Laurent. The Separation Capacity of Random Neural Networks. In: Journal of Machine Learning Research, Vol. 23, no.209, p. 1--47 (2022). (Accepté/Sous presse).

2. Schellekens, Vincent; Jacques, Laurent. Asymmetric Compressive Learning Guarantees With Applications to Quantized Sketches. In: IEEE Transactions on Signal Processing, Vol. 70, no.1, p. 1348-1360 (2022). doi:10.1109/tsp.2022.3157486.

3. Glineur, François; Dong, Shuyu; Gao, Bin; Guan, Yu. New Riemannian Preconditioned Algorithms for Tensor Completion via Polyadic Decomposition. In: SIAM Journal on Matrix Analysis and Applications, Vol. 43, no.2, p. 840-866 (2022). doi:10.1137/21M1394734.

4. Mattenet, Sébastien. An improved finiteness test and a systematic procedure to compute the strong H2 norm of differential algebraic systems with multiple delays. In: Automatica, Vol. 144, no. 110495 (2022). doi:10.1016/j.automatica.2022.110495.

5. Debauche, Virginie; Jungers, Raphaël M.; Della Rossa, Matteo. Comparison of Path-Complete Lyapunov Functions via Template-Dependent Lifts. In: Nonlinear Analysis: Hybrid Systems, (2022). (Soumis).

6. Neves Egidio, Lucas; Jungers, Raphaël M.; Grace S. Deaecto. Stabilization of rank-deficient continuous-time switched affine systems. In: Automatica, (2022). (Accepté/Sous presse).

7. Sivankutty, Siddharth; Rigneault, Hervé; Guérit, Stéphanie; Lee, John Aldo; Jacques, Laurent. Compressive Imaging Through Optical Fiber with Partial Speckle Scanning. In: SIAM Journal on Imaging Sciences, Vol. 15, no.2, p. 387-423 (2022). doi:10.1137/21m1407586.

8. Hendrickx, Julien; Cassandras, Christos.G; Andersson, Sean.B; Pinto, Samuel. C. Multi-Agent Persistent Monitoring of Targets with Uncertain States. In: IEEE Transactions on Automatic Control, (2022). (Accepté/Sous presse).

9. Wierzbiński, Michał; Siła-Nowicka, Katarzyna; Rohm, Witold; Smolak, Kamil; Delvenne, Jean-Charles. The impact of human mobility data scales and processing on movement predictability. In: Scientific Reports, Vol. 11, no.1 (2021). doi:10.1038/s41598-021-94102-x.

10. Delvenne, Jean-Charles; Schaub, Michael. T; Faccin, Mauro. State Aggregations in Markov Chains and Block Models of Networks. In: Physical Review Letters, Vol. 127, no.7 (2021). doi:10.1103/physrevlett.127.078301.

Conference Papers

1. Vary, Simon; Gao, Bin; Ablin, Pierre; Absil, Pierre-Antoine. Optimization flows landing on the Stiefel manifold. In: IFAC-PapersOnLine. Vol. 55, no.30, p. 25-30 (2022). Elsevier BV, 2022 xxx. doi:10.1016/j.ifacol.2022.11.023.

2. Debauche, Virginie; Jungers, Raphaël M.; Della Rossa, Matteo. Characterization of the ordering of path-complete stability certificates with addition-closed templates. 2022 xxx.

3. Delogne, Rémi; Schellekens, Vincent; Jacques, Laurent. ROP inception: signal estimation with quadratic random sketching. 2022 xxx.

4. Sivankutty, Siddharth; Hofer, Matthias; Rigneault, Hervé; Jacques, Laurent; Leblanc, Olivier. An Interferometric view of Speckle Imaging. 2022 xxx.

5. Ren, Wei; Jungers, Raphaël M.. Reachability-based Control Synthesis under Signal Temporal Logic Specifications. In: 2022 American Control Conference, 2022 xxx.

6. Ren, Wei; Jungers, Raphaël M.. Optimal Resource Scheduling and Allocation in Distributed Computing Systems. In: 2021 American Control Conference, 2022, p. 1-8 xxx.

7. Debauche, Virginie; Jungers, Raphaël M.; Della Rossa, Matteo. Necessary and Sufficient Conditions for Template-Dependent Ordering of Path-Complete Lyapunov Methods. In: ACM Conference on Hypertext and Hypermedia. Proceedings. (2022). Association for Computing Machinery, Inc. 2022 xxx.

8. Stollenwerk, Alexander; Sjoerd, Dirksen; Genzel, Martin; Jacques, Laurent. The Separation Capacity of Random Neural Networks. 2021 xxx.

9. Ren, Wei. Razumikhin-type Control Lyapunov and Barrier Functions for Time-Delay Systems. In: 2021 60th IEEE Conference on Decision and Control (CDC), 2021, 978-1-6654-3659-5, p. 5471-5476 xxx. doi:10.1109/cdc45484.2021.9682928.

10. Ren, Wei; Jungers, Raphaël M.. Event-Triggered Tracking Control of Networked and Quantized Control Systems. In: 2021 European Control Conference (ECC), 2021, 978-9-4638-4236-5, p. 632-637 xxx. doi:10.23919/ecc54610.2021.9654945.