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A novel algebraic approach to time-reversible evolutionary models

Autor: Casanellas, Marta, Pons, Roser Homs, Torres, Angélica

In the last years, algebraic tools have been proven useful in phylogenetic reconstruction and model selection through the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too general or t

Externí odkaz: http://arxiv.org/abs/2309.02276

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Primary Ideals and Their Differential Equations

Autor: Roser Homs, Yairon Cid-Ruiz, Bernd Sturmfels

Publikováno v: FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in a polynom

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b33cb121ce675b8aff1c8e958aa67cf1
https://doi.org/10.1007/s10208-020-09485-6

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Bounds on complexity of matrix multiplication away from Coppersmith–Winograd tensors

Autor: Roser Homs, Joachim Jelisiejew, Mateusz Michałek, Tim Seynnaeve

Publikováno v: Journal of Pure and Applied Algebra. 226:107142

We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, and monomial algebras. We analyze them using Strassen's laser method and obtain an upper bound 2.431 on ω. We also explain how in c

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6fe5067b5b5e92c0ca833e8ce10c9bf9
https://doi.org/10.1016/j.jpaa.2022.107142

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Third-Order Moment Varieties of Linear Non-Gaussian Graphical Models

Autor: Carlos Améndola, Mathias Drton, Alexandros Grosdos, Roser Homs, Elina Robeva

In this paper we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combination of its direct causes and independent noise. The underlying direct

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9a0c9ce16c1ea8fdd07356aed19d7d9e

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Computing Maximum Likelihood Estimates for Gaussian Graphical Models with Macaulay2

Autor: Carlos Améndola, Luis David García Puente, Roser Homs, Olga Kuznetsova, Harshit J. Motwani

Publikováno v: JOURNAL OF SOFTWARE FOR ALGEBRA AND GEOMETRY

We introduce the package "GraphicalModelsMLE" for computing the maximum likelihood estimates (MLEs) of a Gaussian graphical model in the computer algebra system Macaulay2. This package allows the computation of MLEs for the class of loopless mixed gr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b8c7e6dba98ceb52ff752770b0bad772
http://arxiv.org/abs/2012.11572

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Canonical Hilbert-Burch matrices for power series

Autor: Roser Homs, Anna-Lena Winz

Sets of zero-dimensional ideals in the polynomial ring $k[x,y]$ that share the same leading term ideal with respect to a given term ordering are known to be affine spaces called Gr\"obner cells. Conca-Valla and Constantinescu parametrize such Gr\"obn

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::304282367a9c7e953ec9bee2c48fbfc4

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On low Gorenstein colength

Autor: Juan Elias, Roser Homs

Publikováno v: Journal of Algebra. 513:368-387

The aim of this paper is to extend the characterization of Teter rings of [9] to Artin rings of Gorenstein colength two and to improve and complete the result [1, Theorem 5.5] on such rings by using Macaulay's inverse system. We provide several expli

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ac20f2266d3a44cd38dd6b1f95626787
https://doi.org/10.1016/j.jalgebra.2018.07.016

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Computing minimal Gorenstein covers

Autor: Roser Homs, Juan Elias, Bernard Mourrain

Publikováno v: Journal of Pure and Applied Algebra
Journal of Pure and Applied Algebra, 2019, ⟨10.1016/j.jpaa.2019.106280⟩
Journal of Pure and Applied Algebra, Elsevier, 2019, ⟨10.1016/j.jpaa.2019.106280⟩

We analyze and present an effective solution to the minimal Gorenstein cover problem: given a local Artin k-algebra A = k 〚 x 1 , … , x n 〛 / I , compute an Artin Gorenstein k-algebra G = k 〚 x 1 , … , x n 〛 / J such that l ( G ) − l (

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cba7331c465fd6e5e8feacabb14a262
https://inria.hal.science/hal-01978906v2/file/EHM_MinimalGorensteinCovers_v2.pdf

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On the Analytic Type of Artin Algebras

Autor: Roser Homs, Juan Elias

Publikováno v: Communications in Algebra. 44:2277-2304

In this paper we give a complete analytic classification of Artin Gorenstein almost stretched algebras, i.e., Artin Gorenstein algebras with Hilbert function {1, n, 2,…, 2, 1,…, 1}.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f568e5c13e2925544dec22b2650ca814
https://doi.org/10.1080/00927872.2015.1027386

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