Breakthrough of directional statistics in space science

Scientific Conference (2023, January 24)

It should be no surprise that already back in the 17-18th centuries important foundations of modern statistical theory were formulated to address astronomical problems, the astronomers were the ... [more ▼]

It should be no surprise that already back in the 17-18th centuries important foundations of modern statistical theory were formulated to address astronomical problems, the astronomers were the statisticians. For instance the 'almost coincidence' in the orbits of the planets in our Solar System with the ecliptic has intrigued the scientists for a long time. Even D. Bernoulli (in the 1730's) wondered if this fact could happen 'by chance'. In a statistical framework, one could think of using a uniformity test on the sphere. Testing isotropy or, equivalently, testing uniformity on the unit hypersphere is one of the oldest as well as most fundamental problems in directional statistics and it is still much considered nowadays. Furthermore with the increasing astronomical data, innovative modern directional statistical theories and models have been proposed to deal with space science issues such as tracking space objects. In this talk, we will provide a review of the many old and recent developments of directional statistics animated by interesting applications in space science. This is a joint work with Christophe Ley. [less ▲]

Machine Learning in Space Weather and how to handle it

Presentation (2022, July 06)

Machine leaning (ML), an imposing but not necessarily new method, is living today its golden age by achieving unforeseen results in numerous industrial applications. On the other side, Space Weather (SW ... [more ▼]

Machine leaning (ML), an imposing but not necessarily new method, is living today its golden age by achieving unforeseen results in numerous industrial applications. On the other side, Space Weather (SW), which describes changing environmental conditions in near-Earth space, is becoming more and more important to our society. But how can SW benefit from the ongoing ML revolution? In the last decade, many researchers, like E. Camporeale, showed that SW possesses all the ingredients often required for a successful ML application. Using this large and freely data set of in situ and remote observations collected over several decades of space missions, it is possible to forecast and nowcast solar activity and thus protect our increasing satellites constellations and us! In this talk, we will give a warm introduction to this field and point out a number of open challenges that we believe is worth to discuss and to undertake. [less ▲]

Solvability of systems of invariant differential equations on H2 and beyond

E-print/Working paper (2022)

We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type G/K can be used for questions of solvability of systems of invariant differential ... [more ▼]

We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type G/K can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander’s proof of the Ehrenpreis-Malgrange theorem. We get complete solvability for the hyperbolic plane H2 and partial results for products H^2 × · · · × H^2 and the hyperbolic 3-space H^3. [less ▲]

Lëtzebuerger Mathematikerin bei der Weltraumagence ESA

Speeches/Talks (2022)

Eng Lëtzebuerger Mathematikerin schafft zanter e puer Woche fir d'europäesch Weltraumagence zu Darmstadt. Déi jonk Fra entwéckelt Modeller fir d'Wieder am Weltall virauszesoen, fir esou d ... [more ▼]

Eng Lëtzebuerger Mathematikerin schafft zanter e puer Woche fir d'europäesch Weltraumagence zu Darmstadt. Déi jonk Fra entwéckelt Modeller fir d'Wieder am Weltall virauszesoen, fir esou d' Satellittesystemer viru Sonnestierm ze schützen. De Weltall passionéiert zanter, datt et d'Mënschheet gëtt. D’Dr. Guenda Palmirotta ass Mathematikerin a huet sech fréi fir dat interesséiert, wat ausserhalb vun der Äerd geschitt. Mam Job bei der Europäescher Weltraumagence geet en Dram an Erfëllung. Zu Darmstadt entwéckelt d'Lëtzebuergerin Modeller fir d’Weltraumwieder virauszesoen. Bestëmmt gëtt dëst vun der Sonn an de Sonnestierm, déi kennen entstoen, déi fir Satellittesystemer e Problem kënnen duerstellen. Ee vun den Ziler ass et, an den nächste Joren d’Previsioune méi präzis ze maachen, ma och méi wäit am viraus kënne viraussoen, wat geschitt. Konkret ginn d’Modeller elo schonn agesat, fir d’Astronauten op der Internationaler Weltraumstatioun ze schützen. Zu Darmstadt huet d'ESA een neien Iwwerwaachungszentral, wou nieft dem Weltraumwieder och aner Elementer vun der Weltraumsécherheet am A behale ginn. Esou zum Beispill de Weltraumschrott, mëttlerweil gëtt et vill Satellitten, déi net fonctionéieren a mat Aktive kéinte kollidéieren. Mat mathematesche Modeller sollen déi aktiv Satellitte gewarnt ginn a se esou hir Positioun fréizäiteg kënnen änneren. [less ▲]

An aspiring career in Space

Article for general public (2022)

Solvability of systems of invariant differential equations on symmetric spaces G/K

Doctoral thesis (2021)

We study the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type. We show how this can be used for questions of solvability of systems of invariant ... [more ▼]

We study the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type. We show how this can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander’s proof of the Ehrenpreis-Malgrange theorem. We get complete solvability for the hyperbolic plane H2 and partial results for finite products H2 × · · · × H2 and the hyperbolic 3-space H3. [less ▲]

MATHEMATICAL CAREERS In Luxembourg and beyond

Diverse speeches and writings (2019)

3D-Foot Plantar Pressure Reconstruction based on the IEE Foot Smart Insole

E-print/Working paper (2017)

Within the growing technology nowadays, the study and research in the human foot have also become much more important. Advanced dynamic foot plantar pressure monitoring applications becomes useful in many ... [more ▼]

Within the growing technology nowadays, the study and research in the human foot have also become much more important. Advanced dynamic foot plantar pressure monitoring applications becomes useful in many healthcare fields, e.g. podiatric and orthopedic applications, rehabilitation tools, sports and fitness training tools. The new IEE1 High- Dynamic (HD) 8-multicells smart sensor provides a single insole-solution for daily usage in order to acquire information on the plantar load distribution for health prophylaxis in a large range of different shoe configurations in real time. Depending on the tracked features, 4, 8 or more sensing cells may be necessary to pick the relevant pressure information. However a high number of cells implies powerful read-out electronics, which in turn implies power consumption challenges and might lead to customer dissatisfaction similarly to the first generation of Apple Smart watch. Knowledge should be built up on the way to get from limited number of cells as relevant information as with a high-resolution sensor. This could be very challenging, because every human has a different unique pressure map, i.e. more phenomenon concentrating in some foot zone location than other person. For example, trying to determine the size and shape of pressure peaks, might require a cluster of samples, whereas the relatively flat surface of the surrounding plain might require only a few. Sophisticated mathematical models will be used to generate the complete high-resolution pressure distribution (HRPD) on each foot based on spatial interpolation schemes. The paper is organized as follows, in Section I we provide an overview of challenges and opportunities around the reconstruction of the 3D Foot Plantar Pressure (FPP). Then in Section II we underlying background needed to understand the human generic gait and describe the new smart insole designed by IEE. In Section III, we develop and apply the spatial interpolation model (SIM) to our underlying problem. Next we discuss and present in Section IV the estimated pressure map based on 3 different approaches, followed by a comparison and validation of their efficiency, reliability and accuracy. In Section V, we use mathematical optimization methods (MOM), e.g. the Particle Swarm Optimization (PSO), in order to determine the optimal location, as well the number of sensors cells needed on the relevant foot pressure information. Finally, Section VI gives the concluding remarks and future work in this topic. [less ▲]

3D-Plantar Foot Pressure Reconstruction based on the new IEE Smart Insole

Bachelor/master dissertation (2017)

Décomposition de Delaunay

Bachelor/master dissertation (2015)

La décomposition de Delaunay standard, par des cercles respectivement par des sphères en dimension supérieure, nous est déjà connue. Par contre la décomposition de Delaunay exotique, par des paraboles et ... [more ▼]

La décomposition de Delaunay standard, par des cercles respectivement par des sphères en dimension supérieure, nous est déjà connue. Par contre la décomposition de Delaunay exotique, par des paraboles et hyperboles en dimension 2 et en dimension supérieure, est encore nouvelle et peu développée. On s’intéressera à l’étudier dans toute sa beauté en nous lançant d’abord dans la partie théorique et ensuite en construisant des programmes qui nous permettront de la manipuler et de la visualiser dans tous les sens. On fera une gamme d’expériences qui nous aidera à mieux comprendre la décomposition pour les différents types. [less ▲]