Posts
Our paper with Alexandros Grosdos, Alexander Heaton, Olga Kuznetsova, Georgy Scholten, and Miruna-Stefana Sorea is now published in Advances in Applied Mathematics. The log-concave maximum likelihood estimate is known to be the exponential of a tent function with the tentpoles being the data points. The tent function induces a subdivision of the convex hull of the data points. It turns out that even determining the optimal subdivision can be challenging! We study the transcendentality of the solutions, give a closed form solution in the simplest case and explore how to certify the solutions.
The European Women in Mathematics General Meeting 2022 took place at Aalto University during August 22-26, 2022. The conference had 129 participants from 25 countries. Click on the post to read more.
The 28th Nordic Congress of Mathematicians took place at Aalto University during August 18-21, 2022. Together with Elisenda Feliu (University of Copenhagen) and Cordian Riener (UiT The Arctic University of Norway), we organized the Applied Algebra Session that brought together applied algebraists in the Nordic countries. The list of talks in the session can be found here.
Together with my PhD student Muhammad Ardiyansyah and Dimitra Kosta we study the model specific embedding problem for symmetric group-based models in phylogenetics. We provide a characterisation of model embeddable Markov matrices corresponding to symmetric group-based phylogenetic models. Our paper is published in the Journal of Mathematical Biology.
My PhD student Olga Kuznetsova won shared Second Place Poster Award at MEGA 2021 for her poster Algebraic Degree of Optimization Over a Variety. The poster is based on our recent preprint Algebraic degree of optimization over a variety with an application to p-norm distance degree together with Olga Kuznetsova and Luca Sodomaco. Congratulations, Olga!
In the joint work with Robert Krone we study the uniqueness of nonnegative matrix factorizations using ideas from the rigidity theory. We give so far the strongest necessary condition for a nonnegative matrix factorization to be unique. Our article has been published in the SIAM Journal of Matrix Analysis and Applications.
In the joint work with Carlos Améndola and Dimitra Kosta we study the maximum likelihood estimation problem for all 2-dimensional Gorenstein toric Fano varieties, we explore the reasons for the ML degree drop and we prove a result about the multiplicativity of ML degrees of codimension zero toric fiber products. This article appeared in the first volume of Algebraic Statistics. This first volume is numbered 11 to honour the past work of the algebraic statistics community.