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Scopus Author ID: 57212573602

Keywords

rough paths, machine learning, deep learning, hopf algebras, signature method

Countries

Germany

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Employment (4)

Humboldt-Universität zu Berlin: Berlin, DE

2024-10-01 to present | Wissenschaftlicher Mitarbeiter (Institut für Mathematik)
Employment
Source: Self-asserted source
Nikolas Tapia

Weierstrass-Institut fur Angewandte Analysis und Stochastik: Berlin, Berlin, DE

2019-05-13 to present | Wissenschaftlicher Mitarbeiter (Stochastic Algorithms and Nonparametric Statistics)
Employment
Source: Self-asserted source
Nikolas Tapia

Technische Universität Berlin: Berlin, Berlin, DE

2019-05-15 to 2022-12-31 | Wissenschaftlicher Mitarbeiter (Institut für Mathematik)
Employment
Source: Self-asserted source
Nikolas Tapia

Norges Teknisk Naturvitenskapelige Universitet Institut for Matematiske Fag: Trondheim, NO

2018-10-01 to 2019-05-31 | PostDoc (Department of Mathematical Sciences)
Employment
Source: Self-asserted source
Nikolas Tapia

Education and qualifications (3)

Laboratoire de Probabilités, Statistique et Modélisation: Paris, Île-de-France, FR

2015-09 to 2018-09-26 | PhD in Mathematics (5ème)
Education
Source: Self-asserted source
Nikolas Tapia

Universidad de Chile Departamento de Ingeniería Matemática: Santiago, CL

2015-04 to 2018-09-26 | PhD in Applied Math.
Education
Source: Self-asserted source
Nikolas Tapia

Facultad de Ciencias Físicas y Matemáticas: Santiago, CL

2007-03 to 2014-01 | Mathematical Engineering (Departamento de Ingeniería Matemática)
Education
Source: Self-asserted source
Nikolas Tapia

Funding (6)

Optimal Control in Energy Markets Using Rough Analysis and Deep Networks

2023-01 to 2023-12 | Grant
Berlin Mathematics Research Center MATH+ (Berlin, DE)
Source: Self-asserted source
Nikolas Tapia

Stochastic and rough aspects in deep neural networks

2021-01 to 2022-12 | Grant
Berlin Mathematics Research Center MATH+ (Berlin, DE)
Source: Self-asserted source
Nikolas Tapia

Stability of Deep Neural Networks

2019-05 to 2020-12 | Grant
Berlin Mathematics Research Center MATH+ (Berlin, DE)
Source: Self-asserted source
Nikolas Tapia

Postdoctoral Position

2018-10 to 2019-09 | Contract
European Research Consortium for Informatics and Mathematics (Sophia Antipolis, FR)
GRANT_NUMBER: 2018-10
Source: Self-asserted source
Nikolas Tapia

Estudiante de Posgrado

2017-09 to 2018-09 | Contract
Núcleo Milenio Modelos Estocásticos de Sistemas Complejos y Desordenados (Santiago, CL)
GRANT_NUMBER: 170217586
Source: Self-asserted source
Nikolas Tapia

Beca Doctorado Nacional 2013

2013-08 to 2017-02 | Grant
Comisión Nacional de Investigación Científica y Tecnológica (Santiago, CL)
GRANT_NUMBER: 21130733
Source: Self-asserted source
Nikolas Tapia

Works (18)

A multiplicative surface signature through its Magnus expansion

2024 | Preprint
DOI: 10.48550/ARXIV.2406.16856
Contributors: Ilya Chevyrev; Joscha Diehl; Kurusch Ebrahimi-Fard; Nikolas Tapia
Source: Self-asserted source
Nikolas Tapia

On expected signatures and signature cumulants in semimartingale models

2024 | Preprint
DOI: 10.48550/ARXIV.2408.05085
Contributors: Peter K. Friz; Paul P. Hager; Nikolas Tapia
Source: Self-asserted source
Nikolas Tapia

Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra

2024-01-12 | Preprint
DOI: 10.48550/ARXIV.2401.06691
Contributors: Leonard Schmitz; Nikolas Tapia
Source: Self-asserted source
Nikolas Tapia

Branched Itô Formula and natural Itô-Stratonovich isomorphism

2023 | Preprint
DOI: 10.48550/ARXIV.2312.04523
ARXIV: 2312.04523
Contributors: Carlo Bellingeri; Emilio Ferrucci; Nikolas Tapia
Source: Self-asserted source
Nikolas Tapia

Generalized iterated-sums signatures

Journal of Algebra
2023-10 | Journal article
DOI: 10.1016/j.jalgebra.2023.06.007
Contributors: Joscha Diehl; Kurusch Ebrahimi-Fard; Nikolas Tapia
Source: check_circle
Crossref
grade
Preferred source (of 2)‎

Shifted substitution in non-commutative multivariate power series with a view toward free probability

SIGMA Symmetry, Integrability and Geometry: Methods and Applications
2023-06-08 | Journal article | Writing - original draft
DOI: 10.3842/SIGMA.2023.038
Contributors: Kurusch Ebrahimi-Fard; Frédéric Patras; Nikolas Tapia; Lorenzo Zambotti
Source: Self-asserted source
Nikolas Tapia

Stability of Deep Neural Networks via Discrete Rough Paths

SIAM Journal on Mathematics of Data Science
2023-03-31 | Journal article
DOI: 10.1137/22M1472358
Contributors: Christian Bayer; Peter K. Friz; Nikolas Tapia
Source: check_circle
Crossref
grade
Preferred source (of 2)‎

Unified signature cumulants and generalized Magnus expansions

Forum of Mathematics, Sigma
2022 | Journal article
DOI: 10.1017/fms.2022.20
Contributors: Peter K. Friz; Paul P. Hager; Nikolas Tapia
Source: check_circle
Crossref

Tropical Time Series, Iterated-Sums Signatures, and Quasisymmetric Functions

SIAM Journal on Applied Algebra and Geometry
2022-12-31 | Journal article
DOI: 10.1137/20M1380041
Contributors: Joscha Diehl; Kurusch Ebrahimi-Fard; Nikolas Tapia
Source: check_circle
Crossref

The geometry of controlled rough paths

2022-03-11 | Preprint
DOI: 10.48550/ARXIV.2203.05946
ARXIV: 2203.05946
Source: Self-asserted source
Nikolas Tapia

The moving frame method for iterated-integrals: orthogonal invariants

Foundations of Computational Mathematics
2022-01-06 | Journal article
DOI: 10.1007/s10208-022-09569-5
Source: Self-asserted source
Nikolas Tapia

Wick polynomials in non-commutative probability

Canadian Journal of Mathematics
2021-08-25 | Journal article
DOI: 10.4153/S0008414X21000407
Source: Self-asserted source
Nikolas Tapia

Transport and continuity equations with (very) rough noise

Partial Differential Equations and Applications
2021-06-21 | Journal article
DOI: 10.1007/s42985-021-00101-y
Source: Self-asserted source
Nikolas Tapia

Hopf-algebraic deformations of products and Wick polynomials

International Mathematics Research Notices
2020-12-06 | Journal article
DOI: 10.1093/imrn/rny269
ARXIV: 1710.00735
Source: Self-asserted source
Nikolas Tapia
grade
Preferred source (of 3)‎

Time-warping invariants of multidimensional time series

Acta Applicandae Mathematicae
2020-05-14 | Journal article
DOI: 10.1007/s10440-020-00333-x
Source: Self-asserted source
Nikolas Tapia
grade
Preferred source (of 4)‎

Iterated-sums signature, quasisymmetric functions and time series analysis

FPSAC 2020
2020-04-30 | Conference paper
Source: Self-asserted source
Nikolas Tapia

The geometry of the space of branched Rough Paths

Proceedings of the London Mathematical Society
2020-03-18 | Journal article
DOI: 10.1112/plms.12311
ARXIV: 1810.12179
Source: Self-asserted source
Nikolas Tapia
grade
Preferred source (of 2)‎

Signatures in Shape Analysis

Geometric Science of Information 2019
2019-08-02 | Book chapter
DOI: 10.1007/978-3-030-26980-7_3
ARXIV: 1906.06406
Source: Self-asserted source
Nikolas Tapia
grade
Preferred source (of 3)‎

Peer review (7 reviews for 6 publications/grants)

Review activity for Analysis and mathematical physics (1)
Review activity for Annales de l'I.H.P. (1)
Review activity for Journal of the Royal Society interface : (2)
Review activity for Quantitative finance. (1)
Review activity for SIAM journal on applied algebra and geometry. (1)
Review activity for Stochastic analysis and applications. (1)
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