Boletín Nº 104
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Boletín del IMI
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1) A Message from the IMI Director
Dear Colleagues,
This week we are bringing forward the publication of issue 104 of the IMI Newsletter to Wednesday, October 11, as tomorrow, Thursday, is a public holiday in Spain. I hope you enjoy its content, which brings many interesting things, as usual.
Ángel Manuel Ramos del Olmo
2) Activities from October 11 to 20, 2023
Seminario de Economía Financiera y Actuarial y Estadística
Title: Premises and analysis of sustainable development factors and rural tourism in Albania
Speaker: Aurora Dibra (University of Shkodra)
Day: October 18, 2023
Place: Room 237, Building 1, Facultad de CC. Económicas y Empresariales
Hour: 12:45
Organized by: Instituto de Matemática Interdisciplinar (IMI) and Departamento de Economía Financiera y Actuarial y Estadística
Seminario de Análisis Matemático y Matemática Aplicada
Title: Daugavet property and diameter two properties in Orlicz-Lorentz spaces
Speaker: Hyung-Joon Tag (Sejong University, Republic of Korea)
Day: October 19, 2023
Place: Room 222
Hour: 13:00
Organized by: Departamento de Análisis Matemático y Matemática Aplicada and Instituto de Matemática Interdisciplinar (IMI)
F.Gallego Lupiáñez. Regularity and paracompactness: Relation in the Field of Fuzziness. Intelligent and Fuzzy Systems. 2023, 65-68. http://dx.doi.org/10.1007/978-3-031-39774-5_8
A. M. Franco-Pereira, M. C. Pardo, C.T. Nakas, B. Reiser. Inference on the symmetry point-based optimal cut-off point and associated sensitivity and specificity with application to SARS-CoV-2 antibody data. Statistics and Operations Research Transactions. 2023, 47, 1. 186-204. Link
Seminario de Análisis Matemático y Matemática Aplicada
Title: Linearization and compactness
Speaker: Mingu Jung (Korea Institute for Advanced Study)
Day: October 24, 2023
Place: Room 222
Hour: 13:00
Organized by: Departamento de Análisis Matemático y Matemática Aplicada and Instituto de Matemática Interdisciplinar (IMI)
Ciclo de conferencias del IMI-DSC
Title: Resource-Driven Activity Networks (RANs) arising from Empirical Adventures at Technion's Service Enterprise Engineering Lab (SEELab)
Speaker: Avishai Mandelbaum (Faculty of Data and Decision Sciences, Technion, Israel)
Day: October 24, 2023
Place: Seminario Sixto Ríos (215), Facultad de CC. Matemáticas, UCM
Hour: 12:30
Organized by: Instituto de Matemática Interdisciplinar (IMI) and Departamento de Estadística e Investigación Operativa
Curso de Doctorado del IMI-DSC
Programa de doctorado IMEIO
Título: Optimización Entera (Integer Optimisation)
Coordinadora: Begoña Vitoriano (Universidad Complutense de Madrid)
Fecha: 23 de octubre - 16 de noviembre, 2023
Place: Seminario Sixto Ríos (215), Facultad de CC. Matemáticas, UCM
Hora: 17:00
Organized by: Instituto de Matemática Interdisciplinar (IMI) y Departamento de Estadística e Investigación Operativa
Defensa de Tesis Doctoral
PhD Candidate: Daniel Luis Rodríguez Vidanes
Title: Geometric, non-linear and set theoretical problems in analysis
Directors: Krzysztof Chris Ciesielski, Gustavo Adolfo Muñoz Fernández and Juan Benigno Seoane Sepúlveda
Program: Investigación Matemática
Day: 25 de octubre, 2023
Place: Sala de Grados (250C), Facultad de CC. Matemáticas
Hour: 12:00
Curso de Doctorado del IMI-DSC
Programa de doctorado IMEIO
Título: Métodos de Decisión Multicriterio
Organizadora: Begoña Vitoriano (Universidad Complutense de Madrid)
Fecha: 20-24 de noviembre, 2023
Lugar: Seminario Sixto Ríos (215)
Hora: 17:00-19:30
Organizado por: Instituto de Matemática Interdisciplinar (IMI) y Departamento de Estadística e Investigación Operativa
5) 1+400. Divulgación con 1 imagen y 400 palabras
Simone Conradi. Eigenvalues experiments
Boletín del IMI, Nº 104 (11 octubre 2023), Sección "1+400. Divulgación con 1 imagen y 400 palabras."
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En esta sección se publican artículos cortos de divulgación, con una imagen y un máximo de 400 palabras (sin tener en cuenta en estas restricciones los datos de los autores). Las personas que quieran publicar un artículo pueden enviarlo a secreadm.imi@mat.ucm.es
La colección de todos los artículos publicados en esta sección se puede ver en www.ucm.es/imi/1mas400
Simone Conradi graduated with honors in theoretical physics in 2004 with a thesis on non-commutative field theories. In 2008, he earned a doctoral degree in theoretical physics from the University of Genoa, where he conducted research on the properties of high-temperature quark-gluon plasma through numerical lattice simulations.
Subsequently, after 10 years of experience in the railway automation sector at Ansaldo STS/Hitachi Rail, where he held various roles including Developer, System Designer, and Work Package Leader, he transitioned to a career as a consultant, applying mathematical models and machine learning algorithms to finance. Currently, he is a computer science teacher at ITIS Delpozzo in Cuneo and is also qualified to teach mathematics and physics. He is actively involved in developing STEM teaching methodologies and in introducing artificial intelligence into school education.
He is author of the book Intelligenza Artificiale, published by Zanichelli.
Among his current scientific interests, we find machine learning, computational physics, and teaching methodologies for STEM subjects.
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Eigenvalues experiments
Simone ConradiITIS Delpozzo in Cuneo
Experimental mathematics is a branch of mathematics that blurs the lines between computation, intuition, and formal proof. It embraces an empirical approach, utilizing computational tools, visualization techniques, and numerical experiments to gain insight into mathematical phenomena, discover patterns, and formulate conjectures. In his work Some Basic Theorems on the Foundations, Kurt Gödel wrote, "If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics." Another eminent mathematician, Jacques Hadamard, believed that mathematical rigor's purpose is to sanction and legitimize the conquests of intuition [1]. In this sense, experimental mathematics is a valuable tool for experimentation and intuition's conquest. Finally, in mathematics education, experimental mathematics facilitates the development of intuition by direct engagement with mathematical objects.
Experimental mathematics heavily relies on computational methods paired with data visualization. In my explorations, I commonly write Python code within Jupyter notebook, which offers tools for numerical computation, data manipulation, symbolic mathematics, and advanced visualization. The exploration discussed in this article originates from the book Computational Discovery on Jupyter [2] and begins by investigating the eigenvalues of matrices constructed through random selection of elements from a finite set of values. The question at the forefront is: what is the distribution of eigenvalues in the ℂ plane when two elements in such matrices are designated as real parameters, t₁ and t₂, and permitted to vary?
There exists an elegant theorem [3], the Gershgorin circle theorem, which delineates a region in the complex plane encompassing all the eigenvalues of a square complex matrix. The Gershgorin region is a union of easily computable and drawable circles using pencil and paper. But what about computing and visualizing eigenvalues?
I endeavored to address this question by creating a Python Jupyter notebook [4], employing NumPy's linear algebra functions and harnessing Matplotlib's visualization capabilities.
The outcome is depicted in the following image.
Each subplot represents eigenvalues in ℂ for individual matrices, each sampled with 500,000 values of t₁ and t₂ within the range [-20, 20] x [-20, 20]. The matrices are randomly generated, with elements drawn from the set {0, -i, i, 1, 1/2}. The two elements replaced by parameters t₁ and t₂ are also randomly selected.
It remains uncertain whether this visualization may yield new insights; it might reveal nothing of significance. Nevertheless, it undeniably constitutes a beautiful piece of mathematical art.
It remains uncertain whether this visualization may yield new insights; it might reveal nothing of significance. Nevertheless, it undeniably constitutes a beautiful piece of mathematical art.
[2] https://computational-discovery-on-jupyter.github.io/Computational-Discovery-on-Jupyter/index.html
[3] Gerschgorin, S. "Über die Abgrenzung der Eigenwerte einer Matrix" Izv. Akad. Nauk. USSR Otd. Fiz.-Mat. Nauk 7, 749-754, 1931.
[4] My Python code: https://github.com/profConradi/eigenfish
Comic strip sent by Ben Orlin and used with permission.
7) Math Puzzle
Puzzle sent by Rik Tangerman
Using one straight cut, divide this triangle in two pieces. Paste them together to construct a parallelogram with perimeter 19.
The solution will be provided in the next issue of Boletin del IMI.
The first cut
Solution to last week's Math Puzzle, sent by Kjartan Poskitt and published on issue No. 103 of the Boletín del IMI:
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