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See detailSolvability of invariant systems of differential equations on the hyperbolic plane
Palmirotta, Guendalina UL

Speeches/Talks (2022)

In the Euclidean case, it is well-known, by Malgrange and Ehrenpreis, that linear differential operators with constant coefficients are solvable. However, what happens, if we genuinely extend this ... [more ▼]

In the Euclidean case, it is well-known, by Malgrange and Ehrenpreis, that linear differential operators with constant coefficients are solvable. However, what happens, if we genuinely extend this situation and consider systems of linear invariant differential operators, is still solvable? In case of Rn (for some positive integer n), the question has been proved mainly by Hörmander. We will show that this remains still true for Riemannian symmetric spaces of non-compact type X = G/K. More precisely, we will present a possible strategy to solve this problem by using the Fourier trans- form and its Paley-Wiener(-Schwartz) theorem for (distributional) sections of vector bundles over X. We will get complete solvability for the hyperbolic plane H2 = SL(2, R)/SO(2) and beyond. This work was part of my doctoral dissertation supervised by Martin Olbrich. [less ▲]

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See detailSolvability of systems of invariant differential equations on H2 and beyond
Palmirotta, Guendalina UL; Olbrich, Martin UL

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 ▲]

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See detailLëtzebuerger Mathematikerin bei der Weltraumagence ESA
Palmirotta, Guendalina UL

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 ▲]

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See detailSpotlight on Young Researchers: Nature’s shapes as mathematical challenges
Palmirotta, Guendalina UL

Article for general public (2022)

In nature, we see hyperbolic forms in corals, flatworms, and many other species of reef organisms, such as sponges and kelps. The hyperbolic spaces are also of interest for mathematicians, who are looking ... [more ▼]

In nature, we see hyperbolic forms in corals, flatworms, and many other species of reef organisms, such as sponges and kelps. The hyperbolic spaces are also of interest for mathematicians, who are looking to prove the solvability of invariant systems of differential equations in unusual spaces such as these. [less ▲]

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See detailAn aspiring career in Space
Palmirotta, Guendalina UL

Article for general public (2022)

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See detailDelorme’s intertwining conditions for sections of homogeneous vector bundles on two and three dimensional hyperbolic spaces
Palmirotta, Guendalina UL; Olbrich, Martin UL

E-print/Working paper (2022)

The description of the Paley-Wiener space for compactly supported smooth functions C_c^∞(G) on a semi-simple Lie group G involves certain intertwining conditions that are difficult to handle. In the ... [more ▼]

The description of the Paley-Wiener space for compactly supported smooth functions C_c^∞(G) on a semi-simple Lie group G involves certain intertwining conditions that are difficult to handle. In the present paper, we make them completely explicit for G = SL(2, R)^d (d ∈ N) and G = SL(2, C). Our results are based on a defining criterion for the Paley-Wiener space, valid for general groups of real rank one, that we derive from Delorme’s proof of the Paley-Wiener theorem. In a forthcoming paper, we will show how these results can be used to study solvability of invariant differential operators between sections of homogeneous vector bundles over the corresponding symmetric spaces. [less ▲]

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See detailA topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on G/K
Palmirotta, Guendalina UL; Olbrich, Martin UL

E-print/Working paper (2022)

We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type X = G/K. We prove a characterisation of their ... [more ▼]

We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type X = G/K. We prove a characterisation of their range. In fact, from Delorme’s Paley-Wiener theorem for compactly supported smooth functions on a real reductive group of Harish-Chandra class, we deduce topological Paley-Wiener and Paley-Wiener- Schwartz theorems for sections. [less ▲]

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See detailSolvability of systems of invariant differential equations on symmetric spaces G/K
Palmirotta, Guendalina UL

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 ▲]

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See detailConference 'SL2R Days'
Palmirotta, Guendalina UL; Voglaire, Yannick; Olbrich, Martin UL

Report (2019)

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See detailMATHEMATICAL CAREERS In Luxembourg and beyond
Palmirotta, Guendalina UL; Notarnicola, Luca UL; Wiese, Gabor UL

Diverse speeches and writings (2019)

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See detailPresentation of a new sensor enabling reliable real time foot plantar pressure distribution retrieval
Melakessou, Foued; Bieck, Werner; Lallemant, Quentin et al

in Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (2017), 247

Monitoring plantar load conditions becomes useful in many health care fields, e.g. podiatric and orthopedic applications, rehabilitation tools, sports and fitness training tools, and in-field diagnosis ... [more ▼]

Monitoring plantar load conditions becomes useful in many health care fields, e.g. podiatric and orthopedic applications, rehabilitation tools, sports and fitness training tools, and in-field diagnosis and prevention tools for posture, balance, loading and contact times monitoring. IEE target is to provide 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 this paper, we introduce for the first time a new High-Dynamic (HD) multi-cell smart insole sensor enabling advanced real-time foot plantar pressure monitoring applications. The in-situ measurement of the dynamic plantar load distribution provides an important new source of information that can be combined with traditional monitoring systems often based on accelerometer and gyroscope sensors. In fact, the new smart insole as presented here, facilitates the discovery in an early phase of any biomechanical mismatch in the walking or running gait of its user. Specific datasets have been recorded from a representative healthy population with different monitoring tools, i.e. force plate, pressure matrix and our new smart insole. The aim was to study the similarity of measurements recorded by each system on a defined measurement protocol. It is shown that the new monitoring device provides a competitive methodology to measure static and dynamic foot plantar pressure distribution. The system flexibility and robustness enable the development of new real-time applications, such as high peak pressure detection for diabetics, activity tracking, etc. The paper is organized as follows: we provide in Sect. 1 an overview of challenges and opportunities around foot pressure monitoring and discuss the sensing capabilities. Then we give a description of the new smart insole designed by IEE in Sect. 2. Next we define in Sect. 3 the measurement protocol based on 3 different systems, followed in Sect. 4 by a comparison of their efficiency and reliability. Finally, Sect. 5 provides related works and Sect. 6 concludes the paper. [less ▲]

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See detail3D-Plantar Foot Pressure Reconstruction based on the new IEE Smart Insole
Palmirotta, Guendalina UL

Bachelor/master dissertation (2017)

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See detail3D-Foot Plantar Pressure Reconstruction based on the IEE Foot Smart Insole
Palmirotta, Guendalina UL; Bordas, Stéphane UL; Melakessou, Foued

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 ▲]

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See detailLuxembourg United Qualification Document for RoboCup 2017
Caire, Patrice; Voos, Holger UL; Medernach, Yan et al

Report (2017)

This is the qualification document for the new team, and first team of Luxembourg, called “Luxembourg United”. This is also the team’s first attempt to qualify for a RoboCup competition. First, a general ... [more ▼]

This is the qualification document for the new team, and first team of Luxembourg, called “Luxembourg United”. This is also the team’s first attempt to qualify for a RoboCup competition. First, a general description of the Luxembourg United team is presented, along with its members and the equipment owned by the team. Second, the mixed team option is considered and potential eventualities suggested. Third, the Luxembourg United team thankfully acknowledges its use of the B-Human code, and lists its original contributions to this code as well as to RoboCup 2017. Fourth, The activities of the team that contribute to Luxembourg United are outlined. Fifth, the impact of the team’s participation and research in RoboCup is described as it applies to the SPL community, to Luxembourg University and SnT Research Center, and to the whole country of Luxembourg. We conclude this document with considerations pertaining to the path that brought us to RoboCup, and present futur perspectives. [less ▲]

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See detailOn the geometry of Householder’s and Halley’s methods
Palmirotta, Guendalina UL

Dissertation and these (2015)

In this paper, some modified Newton’s methods for solving nonlinear equations are proposed. Householder and Halley have suggested a variant of New- ton’s method in which they take an osculating parabola ... [more ▼]

In this paper, some modified Newton’s methods for solving nonlinear equations are proposed. Householder and Halley have suggested a variant of New- ton’s method in which they take an osculating parabola respectively an hyperbola instead of the tangent line. The proposed methods go faster to approximated solution, but it requires more calculation efforts. The order of convergence of both methods is three. By some interesting numerical problems, the theoretical results are illustrated. In the appendix, we give a foretaste of the proposed methods in the complex plane. [less ▲]

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See detailDécomposition de Delaunay
Palmirotta, Guendalina UL

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 ▲]

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