Daniel Perez, PhD.

Experience

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  Laboratoire de Physique Théorique et Hautes Énergies

  Apr 2017 - Jul 2017

  Intern

  — Introduction to the modern calculation methods for multi-loop diagrams in a φ4-theory as well as assisted to a workshop regarding methods and applications of multiloop calculations organized at the Universit ́e Pierre Marie Curie.— Calculation of the β-function and critical exponents of the φ4-model up to two loops.— Study of the applicability of the solutions based on symmetry classes, in particular astudy of the Ising model was performed.

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  Centre de physique théorique

  Apr 2018 - Aug 2018

  Intern

  — Formalized concepts in physics using differential geometry and representation theory.— Derived the Dirac equations based on purely geometrical arguments involving the splitting of universal covariant derivative in a Cartan geometry modeled on(iso(Kn, Q), so(Kn, Q)).— Introduced a graphical method for the calculation of traces of γ-matrices which arise inQuantum Field Theory.— Studied the Einstein-Cartan theory of gravity, which extends General Relativity toinclude spin, which involves the inclusion of torsion.— Applied the dressing field formalism to show that it is possible to achieve spontaneoussymmetry breaking in a gauge invariant manner. Show less

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  Laboratoire Mathématique d'Orsay

  Apr 2019 - Jul 2019

  Intern

  — Abstract study of persistence modules and their applications to topological data analysis (TDA) and geometry— Gave an explicit example of the field dependence of the persistent homology of certain point cloud geometries— Introduction to topological data analysis with the numerical and theoretical analysis of different data sets.

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  Ecole normale supérieure

  Oct 2019 - Jan 2023

  PHD Candidate

  This thesis studies the persistent homology of R-valued continuous functions f on compact topological spaces X. The introduction of homological indices and homological dimensions allows us to link persistence theory to metric quantities of the compact space X, such as its upper-box dimension. These quantities give a precise framework to the Wasserstein p-stability results known in the literature, but also extend them to Hölder functions on more general spaces (including all compact Riemannian manifolds) with explicit constants and whose regime for p is optimal. In degree zero of homology, a more in-depth study can be made using trees associated to f, which generalize the merge trees definable when f is Morse. It is possible to link the dimension of these trees to the persistence index of f and to its barcode. We apply these deterministic results to the stochastic setting to draw consequences about the barcodes of random functions of prescribed regularity. These consequences also allow us to develop distributional discrimination tests for the processes, of which we present a particular example. Finally, we define the ζ-functions associated with a stochastic process and compute these functions and other related quantities for several processes in dimension one, including the Brownian motion and the α-stable Lévy processes. Show less

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  Eco-Adapt

  Jan 2023 - Jun 2024

  Research and Development Project Manager

  As a R&D Project Manager at Eco-Adapt, I have spearheaded cutting-edge data analysis and algorithm design initiatives that have significantly elevated our company's product offerings, whether it be by improving existing algorithms or working on additional features pertinent to Eco-Adapt's market positioning. My work consistently outperforms existing models, delivering real-world impact.Role: 📈 Advanced Algorithm Design: crafting of algorithms that reduce false positives, give confidence bands and reduce uncertainty.📊 Data-Driven Insights: analyze data to inform decisions of maintenance scheduling for clients and improve the accuracy of existing algorithms.🚀 Real-World Success: my contributions have lead to the development of relevant new features to Eco-Adapt's Predict-Adapt solution as well as improvement on current algorithms, both in real-world and bench test data. Show less

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  Qantev

  Jun 2024 - now

  • Fraud, Waste and Abuse - AI Team Lead

    Jan 2025 - now

  • Data Scientist

    Jun 2024 - Jan 2025