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Applied Mathematics (LMAC)

The UTC applied mathe­ma­tics labo­ra­to­ry (UTC-LMAC) is at the core of engi­nee­ring sciences at UTC. LMAC is a trans­dis­ci­pli­na­ry research unit spe­cia­li­sed in inverse pro­blems, sto­chas­tic pro­cesses, digi­tal ana­ly­sis, sta­tis­tics and relia­bi­li­ty, which is a set of pro­blems that depend on socie­tal chal­lenges with indus­trial or socio-eco­no­mic partners.


The UTC Applied Mathe­ma­tics Labo­ra­to­ry is cur­rent­ly deve­lo­ping high level research in applied, deter­mi­nis­tic and sto­chas­tic mathematics.

Its areas of excel­lence lie in appli­ca­tions and deve­lop­ment of effi­cient tools to be used in scien­ti­fic com­pu­ta­tions. These two areas are vie­wed by LMAC as com­ple­men­ta­ry and coherent with UTC's poli­cy to sign varied part­ner­ships, i.e., bet­ween UTC's labo­ra­to­ries as well as rele­vant exter­nal research teams.

Research teams and thematics

LMAC's research port­fo­lio addresses 2 main sets of problems:

  • inverse pro­blems ;
  • sto­chas­tic systems.

These pro­blems, both from a theo­re­ti­cal and from an applied point of view, arise in ques­tions faced by engi­neers in applied sciences and engi­nee­ring in general.

The the­ma­tics and appli­ca­tions are as follows:

  • Inverse and bad­ly for­mu­la­ted pro­blems (IP): Iden­ti­fi­ca­tion of para­me­ters, data Infilling, fluid-struc­ture Inter­ac­tions, vali­di­ty tes­ting in dif­fu­sion pro­blems, shape and topo­lo­gy optimization.
  • Sto­chas­tic Sys­tems (S2): Semi-Mar­kov pro­cesses, sta­bi­li­ty fac­tors and sta­tio­na­ry condi­tions, non para­me­tric eva­lua­tion, non-para­me­tric and semi-para­me­tric test protocols.
  • Recent (or ongoing) Appli­ca­tions: Elec­tro-ence­pha­lo­grams (EEG), opti­cal tomo­gra­phy (inverse NIRS), crack pro­pa­ga­tion, dis­lo­ca­tion phe­no­me­na, saline intru­sion, atmos­phe­ric pol­lu­tion, iden­ti­fi­ca­tion of meta­bo­lic flow in plants, inter­nal com­bus­tion engine model­ling, relia­bi­li­ty, per­for­mance and sta­bi­li­ty of com­plex sys­tems, ran­dom net­works and tele­com­mu­ni­ca­tions, epi­de­mio­lo­gy, Baye­sian Model­ling of bio­lo­gi­cal gene net­works, seis­mo­lo­gy, DNA Modelling.


Partenariats à l'UTC

UTC-LMAC is deve­lo­ping part­ner­ships with indus­trial part­ners (Renault, Saint-Gobain, Total, Valeo…), and plu­ri­dis­ci­pli­na­ry col­la­bo­ra­tions (medi­cine, bio­lo­gy, mecha­ni­cal engi­nee­ring,…) that asso­ciates seve­ral UTC research units and teams. (Rober­val, BMBI). In 2017, LMAC and the Rober­val labo­ra­to­ry joi­ned forces to form a com­mon col­la­bo­ra­tive research platform.

The LMAC leads an inter-team and inter-labo­ra­to­ry wor­king group on redu­ced-order modeling.

Partnerships in France

Uni­ver­si­té de Picar­die Jules Verne (UPJV), uni­ver­si­té de Reims Cham­pagne-Ardenne (URCA), École natio­nale des Ponts et Chaus­sées (ENPC), Ins­ti­tut natio­nal de recherche en infor­ma­tique et en auto­ma­tique (INRIA), École natio­nale de la sta­tis­tique et de l'administration éco­no­mique (ENSAE), Télé­com Paris, uni­ver­si­té de Lille 1, uni­ver­si­té de Paris 13, École natio­nale supé­rieure de chi­mie, de bio­lo­gie et de phy­sique (ENSCBP, Bor­deaux), École natio­nale supé­rieure d'arts et métiers (ENSAM, Bor­deaux), uni­ver­si­té de Marne-la-Val­lée, uni­ver­si­té de Rouen, uni­ver­si­té de Lille 3.

Partnerships abroad

Uni­ver­si­té La-Sapien­za (Rome, Ita­lie), Saint Peters­burg State Elec­tro­tech­ni­cal Uni­ver­si­ty (Rus­sie), uni­ver­si­té de McMas­ter (Cana­da), uni­ver­si­té de Cal­ga­ry (Cana­da), uni­ver­si­té de Lis­bonne (Por­tu­gal), uni­ver­si­té Aris­tote de Thes­sa­lo­nique (Grèce), uni­ver­si­té de Patras (Grèce),uUni­ver­si­té de Gre­nade (Espagne), Ins­ti­tut de mathé­ma­tiques de l'académie des sciences d'Ukraine, Charles Uni­ver­si­ty (Répu­blique tchèque), École natio­nale des arts et métiers (Mek­nès, Maroc), École poly­tech­nique (Tunis, Tuni­sie), Uni­ver­si­té Poli­teh­ni­ca (Buca­rest, Rou­ma­nie), uni­ver­si­té de Debre­cen (Hon­grie), Uni­ver­si­té Liba­naise (Tri­po­li, Liban), New York Uni­ver­si­ty (États-Unis).


The LMAC research team is cur­rent­ly deve­lo­ping nume­rous other pro­jects with its aca­de­mic part­ners in France and abroad.

The PSPC project

VALODIM which covers the opti­mal value of diges­tates from metha­ni­sa­tion pro­cess, is a pro­gramme that aims struc­tu­ring a natio­nal sec­tor to valo­rise diges­tates by crea­ting and orga­ni­zing local eco-sys­tems for the pro­duc­tion of orga­nic fertilizers.

ITE PIVERT, programme Genesys

Meta­Lip­Pro-PL1 consti­tutes a know­ledge acqui­re­ment phase that will enable the research teams to improve and com­plete our know­ledge about lipoid meta­bo­lism for plants and for yeasts. Ano­ther aim is to esta­blish the bases for the pur­pose of deve­lo­ping a pilot plat­form for lipid pro­duc­tion and extraction.


One of the objec­tive of the PHASEFIELD pro­ject is to desi­gn inno­va­tive digi­tal phase field methods applied to the deve­lop­ment and opti­mi­za­tion of new materials.

Sorbonne university cluster project

The gene­ral objec­tive of the ROBUST pro­ject is to stu­dy sta­bi­li­ty of cell cycles in the pre­sence of a sto­chas­tic noise, using obser­va­tions that relate to growth of "silk sen­sor whis­kers" on may­fly thoraxes.

Zoom on a project

Over recent decades, we have seen the arri­val of nume­rous medi­cal ima­ging tech­niques, often indeed being com­ple­men­ta­ry with each other. Neu­ro­phy­sio­lo­gists, bio­phy­si­cists, radio­lo­gists, image treat­ment spe­cia­lists, alrea­dy col­la­bo­rate to detect and pin­point patho­lo­gi­cal sources in the brain. In a very near future, mathe­ma­ti­cians will join forces with these afo­re­men­tio­ned experts.

Mathe­ma­ti­cal treat­ment allows you to syn­the­sis all the data made avai­lable by various tech­niques cur­rent­ly employed on patients. "Our labo­ra­to­ry" explains Abdel­la­tif El Badia, Direc­tor of LMAC, "tackles this issue of pin­poin­ting the sources for patho­lo­gi­cal brain acti­vi­ties by trea­ting it as an inverse pro­blem. Expe­ri­men­tal data allow us to pro­gress 'back­wards' up to the sources, using mathe­ma­ti­cal models." In order to be able to do this, mathe­ma­ti­cians use the stan­dard elec­troen­ce­pha­lo­gram, the MRI which in essence 'draws' the brain contours and also Near Infra-Red Spec­tro­sco­py (NIRS) using lumi­nous sources in the near infra-red spec­trum. "When a brain reveals an epi­lep­tic acti­vi­ty, there is a conco­mi­tant change in the blood flow rates and varia­tions in the concen­tra­tion levels of oxy­ge­na­ted and deoxy­ge­na­ted hae­mo­glo­bins and these are revea­led by the NIRS – cer­tain areas of the brain will beseen to absorb more light than others and this is where the patho­lo­gy is occur­ring", adds Abdel­la­tif El Badia.

It now remains for the LMAC research team to try to com­bine the expe­ri­men­tal fin­dings and data, using a nume­ri­cal model that would lead on to a spe­ci­fic soft­ware package that would allow the doc­tors to accu­ra­te­ly locate and posi­tion the exact source of the patho­lo­gy. Cli­ni­cal tests at the near­by regio­nal tea­ching hos­pi­tal at Amiens (CHU-Amiens) should enable this research to pro­gress fair­ly rapidly.

Contact and documentation

Contacts de la recherche à l'UTC

Direc­teur du labo­ra­toire LMAC
Flo­rian De Vuyst
 +33 (0)3 44 23 46 88
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