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karhunenloeve/README.md

📃 Papers

  1. Luciano Melodia and Richard Lenz (2022): Homological Time Series Analysis of Sensor Signals from Power Plants. Machine Learning for Irregular Time Series. Machine Learning and Principles and Practice of Knowledge Discovery in Databases. In Michael Kamp, Irena Koprinska, Adrien Bibal et al. (ed.): Communications in Computer and Information Science. Springer Nature, Switzerland.
  2. Luciano Melodia and Richard Lenz(2021): Estimate of the Neural Network Dimension Using Algebraic Topology and Lie Theory. Image Mining. Theory and Applications VII. Pattern Recognition and Information Forensics. In Alberto Del Bimbo, Rita Cucchiara, Stan Sciaroff et al. (ed.): Lecture Notes in Computer Science. Springer Nature, Switzerland
  3. Luciano Melodia and Richard Lenz (2020): Persistent Homology as Stopping-Criterion for Voronoi Interpolation. Proceedings of the International Workshop on Combinatorial Image Analysis. In Tibor Lukić, Reneta Barneva, Valentin Brimkov et al. (ed.): Lecture Notes in Computer Science. Springer, Cham.
  4. Luciano Melodia (2015): Zur Verwendung des Paradigmas brauchen mit und ohne zu mit Infinitiv. In KateĆĄina Ć ichovĂ , Reinhard Krapp, Rössler Paul et al. (ed.): StandardvarietĂ€t des Deutschen – Fallbeispiele aus der sozialen Praxis, Logos, Berlin.

📓 Preprints

  1. Luciano Melodia (2025): Spectral Sequences - Leray-Serre Spectral Sequence. Graduate Seminar on Spectral Theory in Mathematical Physics, Friedrich-Alexander UniversitĂ€t Erlangen-NĂŒrnberg.
  2. Luciano Melodia (2024): BeschrĂ€nkte Fremdholmoperatoren und deren Fremdholmindex auf separablen HilbertrĂ€umen. Graduate Seminar on Spectral Flow in Functional Analysis, Friedrich-Alexander UniversitĂ€t Erlangen-NĂŒrnberg.
  3. Luciano Melodia (2023): Notes on Simplicial and Singular Homology. Graduate Seminar on Topics in Topology, Friedrich-Alexander UniversitĂ€t Erlangen-NĂŒrnberg.
  4. Luciano Melodia (2023): NatĂŒrliche Transformationen, Äquivalenzen von Kategorien, darstellbare Funktoren und das Lemma von Yoneda. Graduate Seminar on Sheaf Theory, Friedrich-Alexander UniversitĂ€t Erlangen-NĂŒrnberg.

📔 Theses

  1. Luciano Melodia (2024): Algebraic and Topological Persistence. Bachelor Thesis in Mathematics supervised by Prof. Ph.D. Kang Li, Library of the Friedrich-Alexander UniversitĂ€t Erlangen-NĂŒrnberg.
  2. Luciano Melodia (2016): Deep Learning SchĂ€tzung zur absorbierten Strahlungsdosis fĂŒr die nuklearmedizinische Diagnostik. Master Thesis in Information Science supervised by Prof. Dr. rer. nat. Elmar Lang, Library of the University of Regensburg.

Popular repositories Loading

  1. MADVK MADVK Public archive

    Deep Learning Estimation of Absorbed Dose for Nuclear Medicine Diagnostics.

    Python 3 2

  2. TopoData TopoData Public archive

    Lecture notes for Topological Data Analysis.

    TeX 3

  3. NTOPL NTOPL Public archive

    Estimation of Neural Network Dimension using Algebraic Topology and Lie Theory.

    Python 2

  4. TwirlFlake TwirlFlake Public archive

    Homological Time Series Analysis of Sensor Signals from Power Plants.

    Python 2

  5. SIML SIML Public archive

    Persistent Homology as Stopping-Criterion for Voronoi Interpolation.

    TeX 1

  6. TopoSheaf TopoSheaf Public archive

    Handout and notes for a seminar in topology hold at FAU with focus on sheaf theory.

    TeX 1