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PEOPLE@HES-SO – Directory and Skills inventory

PEOPLE@HES-SO
Directory and Skills inventory

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Wasem Micha

Wasem Micha

Assoziierter Professor FH

Main skills

Mathematics

Geometry

Français

Deutsch

English

Higher Education

  • Contact

  • Teaching

  • Research

  • Publications

Main contract

Assoziierter Professor FH

Phone: +41 26 429 67 22

Desktop: HEIA_D30.03

Haute école d'ingénierie et d'architecture de Fribourg
Boulevard de Pérolles 80, 1700 Fribourg, CH
HEIA-FR
Institute
iSIS - Institut des systèmes intelligents et sécurisés
BA HES-SO en Architecture - Haute école d'ingénierie et d'architecture de Fribourg
  • Mathematik
BSc HES-SO en Génie civil - Haute école d'ingénierie et d'architecture de Fribourg
  • Analyse 1 à 3
BSc HES-SO en Génie électrique - Haute école d'ingénierie et d'architecture de Fribourg
  • Algèbre linéaire 1 et 2
  • Analyse 1 à 4
BSc HES-SO en Génie mécanique - Haute école d'ingénierie et d'architecture de Fribourg
  • Algèbre linéaire 1 et 2
  • Analyse 1 à 3
BSc HES-SO en Chimie - Haute école d'ingénierie et d'architecture de Fribourg
  • Lineare Algebra

Ongoing

FRISAM-Swisslos-2021

Role: Collaborator

Description du projet :

Modellierung und statistrische Analyse eines Spiels

Research team within HES-SO: Wasem Micha

Statut: Ongoing

Big Skill V1.8

Role: Collaborator

Description du projet :

Statistische Analyse und Modellierung eines Spielautomaten

Research team within HES-SO: Wasem Micha

Statut: Ongoing

Completed

BeyondBézier

Role: Collaborator

Description du projet :

In the early age of digital type, several methods were explored to draw letterforms. One of them, the Bézier spline, an algorithm
that generates curves with a small quantity of data, has the crucial advantage of sparing computer memory and processing
resources. It is today the industry standard. This project aims to question and reevaluate it, to move beyond established trends, to
develop innovative ideas by exploring alternative methods of drawing curves, and letterforms.

Research team within HES-SO: Wasem Micha

Durée du projet: 01.09.2023 - 28.02.2025

Montant global du projet: 195'560 CHF

Statut: Completed

Amélioration des techniques de Metamodeling appliquées à la géotechnique
AGP

Role: Main Applicant

Financement: HES-SO Rectorat

Description du projet : Dans de nombreux domaines de l'ingénierie, notamment en ingénierie civile et particulièrement en géotechnique, la prédiction de grandeurs physiques telles que le champ de déplacements ou de contraintes fait partie intégrante du cahier des charges de l'ingénieur. Depuis deux décennies, la puissance de calcul des ordinateurs permet aux spécialistes d'effectuer des simulations numériques toujours plus pointues. Dans ces différentes méthodes, c'est la simulation par éléments finis (FE) qui s'est standardisée car elle permet de résoudre des problèmes ne possédant pas de solution analytique. Toutefois, la méthode des éléments finis ne permet d'obtenir qu'une solution discrète uniquement valable pour une certaine combinaison de paramètres d'input. De plus, certains modèles géotechniques, comme des problèmes avec couplage hydromécanique ou tridimensionnels, nécessitent des temps de résolution qui peuvent aisément atteindre plusieurs heures, voire jours. Dans un cadre d'analyse numérique, l'obtention d'une solution continue à partir d'un modèle aux éléments finis peut se faire par une interpolation des solutions discrètes. Ceci se traduit sur base d'une approximation par méta-modèles. Pour des modèles légèrement non linéaires, les techniques actuelles permettent une approximation fiable de la solution du modèle FE. A l'inverse, les modèles FE fortement non linéaires comportent des zones dans lesquelles les méta-modèles actuels ont des difficultés à approcher la solution. L'état de l'art actuel sur les techniques de méta-modèles place la boîte à outils UQLab, développée à l'ETH Zürich, comme référence dans cette matière. C'est donc à l'aide de cette boîte à outils que nous proposons de travailler. L'objectif du projet est d'améliorer l'état de l'art de deux manières. Premièrement nous allons proposer un échantillonnage alternatif en le dissociant de la distribution de probabilité des paramètres d'entrée. Il est bien connu ' par exemple pour des problèmes unidimensionnels ' qu'un choix judicieux des points d'échantillonnage influencera la vitesse de convergence de l'interpolant, donc le choix des points est un aspect important à exploiter afin de maximiser la qualité du méta-modèle. Deuxièmement, il y a des modèles dans le domaine de la géotechnique qui admettent différents régimes qui se caractérisent par des singularités au niveau des gradients. Il est proposé ici de créer des méta-modèles région par région, qui seront finalement recollés les uns aux autres. Dans une dernière phase exploratoire, nous voulons examiner si une détection de différentes régions est réalisable. L'explication et la validation de notre méthodologie fera l'objet d'un rapport détaillé et d'un article scientifique. L'intérêt pour des méta-modèles fiables ne se limite pas au domaine de la géotechnique. Dans de nombreux contextes où les modèles analytiques ne sont pas disponibles, l'utilisation de méta-modèles est une solution efficace pour : obtenir des approximations fiables du modèle original, effectuer des calculs probabilistes ou proposer des optimisations sur le système initial.

Research team within HES-SO: Wasem Micha , Minini Jocelyn

Partenaires académiques: FR - EIA - Institut iSIS

Durée du projet: 01.03.2024 - 28.02.2025

Montant global du projet: 99'980 CHF

Statut: Completed

Autonomous Vehicles Project

Role: Co-applicant

Description du projet :

In 2017, Shalev-Schwartz, Shammah and Shashua published an article on the preprint server arXiv entitled «On a Formal Model of Safe and Scalable Self-driving Cars». In this paper, a deterministic safety model called RSS is introduced and the article claims that if every road user adheres to the rules given by RSS, then no accidents can happen. The goal of this project was to inspect the article and to either validate the model or to find counterexamples to the claims made therein. Although the approach presented in the article seems promising, we were able to find shortcomings of the work by constructing scenarios in which RSS does not provide a guarantee for no accidents. Furthermore, we detected lines of thought along which the model could be refined.

Joint work with Corinne Hager Jörin and Florence Yerly.

Research team within HES-SO: Wasem Micha

Durée du projet: - 09.07.2020

Statut: Completed

2025

Counting nodes in Smolyak grids
Scientific paper ArODES

Jocelyn Minini, Micha Wasem

Ars Combinatoria,  2025, 162, 149-157

Link to the publication

Summary:

Using generating functions, we are proposing a unified approach to produce explicit formulas, which count the number of nodes in Smolyak grids based on various univariate quadrature or interpolation rules. Our approach yields, for instance, a new formula for the cardinality of a Smolyak grid, which is based on Chebyshev nodes of the first kind and it allows to recover certain counting-formulas previously found by Bungartz-Griebel, Kaarnioja, Müller-Gronbach, Novak-Ritter and Ullrich.

2024

A short proof of a variant of the round-robin scheduling problem
Scientific paper ArODES

Chris Busenhart, Christoph Leuenberger, Micha Wasem, Micha Wasem

Elemente der Mathematik,  To be published.

Link to the publication

Summary:

Suppose 2n people participate in a sports tournament that consists of multiple rounds. In each round, two teams of n people are formed to play against each other. We require that every two players play at least once in opposing teams and once in the same team. For this variant of the round-robin scheduling problem, an explicit formula for the minimum number of rounds needed to satisfy both conditions has recently been published. In this short note, an alternative and short proof of this is given.

2022

Polyfunctions over commutative rings
Scientific paper ArODES

Ernst Specker, Norbert Hungerbühler, Micha Wasem

Journal of Algebra and Its Applications,  2024, 23, 1, 2450014

Link to the publication

Summary:

A function f:R→R, where R is a commutative ring with unit element, is called polyfunction if it admits a polynomial representative p∈R[x]. Based on this notion, we introduce ring invariants which associate to R the numbers s(R) and s(R′;R), where R′ is the subring generated by 1. For the ring R=Z/nZ the invariant s(R) coincides with the number theoretic Smarandache or Kempner functions(n). If every function in a ring R is a polyfunction, then R is a finite field according to the Rédei–Szele theorem, and it holds that s(R)=|R|. However, the condition s(R)=|R| does not imply that every function f:R→R is a polyfunction. We classify all finite commutative rings R with unit element which satisfy s(R)=|R|. For infinite rings R, we obtain a bound on the cardinality of the subring R′ and for s(R′;R) in terms of s(R). In particular we show that |R′|≤s(R)!. We also give two new proofs for the Rédei–Szele theorem which are based on our results.

The ring of polyfunctions over Z/nZ
Scientific paper ArODES

Ernst Specker, Norbert Hungerbühler, Micha Wasem

Communications in Algebra,  2022

Link to the publication

Summary:

We study the ring of polyfunctions over Z/nZ. The ring of polyfunctions over a commutative ring R with unit element is the ring of functions f:R→R which admit a polynomial representative p∈R[x] in the sense that f(x)=p(x) for all x∈R. This allows to define a ring invariant s which associates to a commutative ring R with unit element a value in N∪{∞}. The function s generalizes the number theoretic Smarandache function. For the ring R=Z/nZ we provide a unique representation of polynomials which vanish as a function. This yields a new formula for the number Ψ(n) of polyfunctions over Z/nZ. We also investigate algebraic properties of the ring of polyfunctions over Z/nZ. In particular, we identify the additive subgroup of the ring and the ring structure itself. Moreover we derive formulas for the size of the ring of polyfunctions in several variables over Z/nZ, and we compute the number of polyfunctions which are units of the ring.

2021

Equilibria of plane convex bodies
Scientific paper ArODES

Jonas Allemann, Norbert Hungerbühler, Micha Wasem

Journal of Nonlinear Science,  2021, vol. 31, article no. 86

Link to the publication

Summary:

We obtain a formula for the number of horizontal equilibria of a planar convex body K with respect to a center of mass O in terms of the winding number of the evolute of ∂K with respect to O. The formula extends to the case where O lies on the evolute of ∂K and a suitably modified version holds true for non-horizontal equilibria.

Equidimensional isometric extensions
Scientific paper ArODES

Micha Wasem

Zeitschrift für Analysis und ihre Anwendungen,  2021, vol. 3, pp. 349-366

Link to the publication

Summary:

Let Σ be a hypersurface in an n-dimensional Riemannian manifold M, n≥2. We study the isometric extension problem for isometric immersions f:Σ→Rn, where Rn is equipped with the Euclidean standard metric. We prove a general curvature obstruction to the existence of merely differentiable extensions and an obstruction to the existence of Lipschitz extensions of f using a length comparison argument. Using a weak form of convex integration, we then construct one-sided isometric Lipschitz extensions of which we compute the Hausdorff dimension of the singular set and obtain an accompanying density result. As an application, we obtain the existence of infinitely many Lipschitz isometries collapsing the standard two-sphere to the closed standard unit 2-disk mapping a great-circle to the boundary of the disk.

2020

On absolute and relative change
Scientific paper ArODES

Micha Wasem, Silvan Brauen, Philipp Erpf

SSRN,  PREPRINT

Link to the publication

Summary:

Based on an axiomatic approach we propose two related novel oneparameter families of indicators of change which put in a relation classical indicators of change such as absolute change, relative change and the log-ratio.

2019

Non-integer valued winding numbers and a generalized residue theorem
Scientific paper ArODES

Norbert Hungerbühler, Micha Wasem

Journal of Mathematics,  2019, vol. 2019

Link to the publication

Summary:

We define a generalization of the winding number of a piecewise C1 cycle in the complex plane which has a geometric meaning also for points which lie on the cycle. The computation of this winding number relies on the Cauchy principal value but is also possible in a real version via an integral with bounded integrand. The new winding number allows to establish a generalized residue theorem which covers also the situation where singularities lie on the cycle. This residue theorem can be used to calculate the value of improper integrals for which the standard technique with the classical residue theorem does not apply.

2018

An integral that counts the zeros of a function
Scientific paper ArODES

Norbert Hungerbühler, Micha Wasem

Open Mathematics,  2018, vol. 16, no. 1

Link to the publication

Summary:

Given a real function f on an interval [a, b] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f , f’ and f’’. In particular, by approximating the integral with the trapezoidal rule on a fine enough grid, we can compute the number of zeros of f by evaluating finitely many values of f , f’ and f’’. A variant of the integral even allows to determine the number of the zeros broken down by their multiplicity.

2017

Convex Integration and Legendrian Approximation of Curves
Scientific paper

Wasem Micha

Journal of Convex Analysis, 2017 , no  24, pp.  309-317

Link to the publication

The One-Sided Isometric Extension Problem
Scientific paper

Wasem Micha

Results in Mathematics, 2017 , no  71, pp.  749-781

Link to the publication

2016

h-Principle for Curves with Prescribed Curvature
Scientific paper

Wasem Micha

Geometriae Dedicata, 2016 , no  184, pp.  135-142

Link to the publication

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