Using mathematical optimization, to fly Internet balloons and to detect heart disorders

As Johan Mathe sees things — he inci­den­tal­ly is mad keen on math­e­mat­i­cal opti­miza­tion (and a recent UTC grad­u­ate) — var­i­ous com­plex prob­lems can be solved using a sim­i­lar method­olog­i­cal approach: i.e., you opti­mize the sys­tem to attain an accept­able solu­tion. The mod­el used to move and posi­tion Google Inter­net anten­nae is close to the algo­rithm devel­oped to detect and clas­si­fy car­diac mal for­ma­tion using an ultra­son­ic sen­sor input. 

Does Google ever do things like any­one else? In the Gog­gle X research labs near San Fran­cis­co, any new project will be deemed wor­thy if and when the devel­op­ment can­not demon­strate that it will not work. “Take the Loon project the aim of which is to pro­vide Inter­net access to 4 bil­lion peo­ple on Earth (who today have no con­nec­tions), the idea is to place heli­um bal­loons in the stratos­phere; the ini­tial project team tried to demon­strate that it was impos­si­ble to posi­tion these relay bal­loons – hun­dreds would be need­ed — with suf­fi­cient accu­ra­cy”, explains Johan Mathe, UTC grad­u­ate and for­mer engi­neer on the Google Loon team. 

Accu­ra­cy need­ed: bet­ter than 200 km Hav­ing the bal­loons change alti­tude to make use of winds is the only way to move and posi­tion these anten­nae bal­loons accu­rate­ly so they can act as relays for mobile phones. For sev­er­al years, the R&D team mod­elised and exper­i­ment­ed the set-up, try­ing to show the extreme dif­fi­cul­ty met with these bal­loons (15m diam­e­ter!) fly­ing some 20 km above the Earth. “The project was almost aban­doned because we could not hold a posi­tion with an accu­ra­cy bet­ter than 200 km, where­as the trans­mis­sion range is less than 40 km”, under­lines Johan Mathe 

A local approach

But just at the time the team was about to demon­strate that the pro­gramme was not fea­si­ble, two inno­va­tions changed the deal. “The first idea con­sist­ed of using atmos­pher­ic winds to change the bal­loon height and make it move lat­er­al­ly”, explains Johan Mathe who wrote the algo­rithm that enabled the bal­loon to move “upwind” (when the wind a pri­ori was blow­ing the wrong way!). Con­trol­ling var­i­ous wind lev­els calls for a pre­cise knowl­edge of local weath­er con­di­tions. The sec­ond idea con­sist­ed of using the bal­loons them­selves to col­lect and trans­mit the data need­ed via on-board sen­sor devices. 

The result was an accu­ra­cy of 500 m for a bal­loon in flight between New Zealand and Chile. The flight con­tin­ued for anoth­er 3 months, dur­ing which the bal­loon accom­plished sev­er­al rev­o­lu­tions of the Earth. 

From balloons to cardiac malformation

The work was a suc­cess for Google and also for the math­e­mat­i­cal opti­miza­tion meth­ods imple­ment­ed by Johan Mathe to com­pute the bal­loon tra­jec­to­ries and a high com­plex and uncer­tain milieu. “The opti­miza­tion tools I used here can poten­tial­ly be applied to all sorts of dif­fer­ing prob­lems”, explains our UTC grad­u­ate, who chose to leave Google and move to anoth­er area: detec­tion of car­diac mal­for­ma­tion using echog­ra­phy, with the view to pre­vent­ing future heart dis­or­ders from occur­ring. Johan was all the more sen­si­tive to this field because of fam­i­ly cas­es, and he was recruit­ed by Bay­labs who were devel­op­ing recog­ni­tion algo­rithms base on ‘deep-learn­ing” process­es, which is an inno­v­a­tive area for auto­mat­ic learn­ing pro­to­cols. “The process­es relay on very effi­cient visu­al recog­ni­tion tools which are used both for self-dri­ve cars to pho­to analy­sis and man­age­ment tech­niques”, under­lines Johan Mathe. Again, from Johan’s point of view, rec­og­niz­ing a mal­for­ma­tion con­sists of opti­miz­ing its iden­ti­fi­ca­tion from among a set of pos­si­ble results. 

Echo-graph­ics is an inex­pen­sive way to analyse par­ents’ con­di­tions, and the devel­op­ment of a tool that helps non-spe­cial­ists – such as the GPs – to eas­i­ly detect a heart con­di­tion rep­re­sents a great progress in this field. It is all the more impor­tant that heart dis­eases are a major fac­tor for mor­tal­i­ty and numer­ous abnor­mal con­di­tions can only be detect­ed today by spe­cial­ists using expen­sive equipment. 

Math­e­mat­i­cal opti­mi­sa­tion, whether it be applied to stratos­pher­ic bal­loons or to detec­tion of heart mal­for­ma­tions, is almost mag­i­cal in the sense that the same degree of for­mal pre­sen­ta­tion and analy­sis allow very dif­fer­ent phys­i­cal sit­u­a­tions to be assessed. 

Le magazine

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