Zobrazeno 1 - 10
of 484
pro vyhledávání: '"SATTELBERGER, A. P."'
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space wavefunction. T
Externí odkaz:
http://arxiv.org/abs/2410.14757
The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such group act
Externí odkaz:
http://arxiv.org/abs/2309.13736
Feynman integrals are solutions to linear partial differential equations with polynomial coefficients. Using a triangle integral with general exponents as a case in point, we compare $D$-module methods to dedicated methods developed for solving diffe
Externí odkaz:
http://arxiv.org/abs/2303.11105
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We present algo
Externí odkaz:
http://arxiv.org/abs/2301.02512
We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated using tools
Externí odkaz:
http://arxiv.org/abs/2208.08967
Publikováno v:
SIAM Journal on Applied Algebra and Geometry 7 (2023) 77-103
We explore the positive geometry of statistical models in the setting of toric varieties. Our focus lies on models for discrete data that are parameterized in terms of Cox coordinates. We develop a geometric theory for computations in Bayesian statis
Externí odkaz:
http://arxiv.org/abs/2204.06414
We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate polynomial ring arising from the hierarchical stabilization of the ze
Externí odkaz:
http://arxiv.org/abs/2112.06509
Autor:
Breiding, Paul, Çelik, Türkü Özlüm, Duff, Timothy, Heaton, Alexander, Maraj, Aida, Sattelberger, Anna-Laura, Venturello, Lorenzo, Yürük, Oğuzhan
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration spaces of frame
Externí odkaz:
http://arxiv.org/abs/2103.16300
We link $n$-jets of the affine monomial scheme defined by $x^p$ to the stable set polytope of some perfect graph. We prove that, as $p$ varies, the dimension of the coordinate ring of a certain subscheme of the scheme of $n$-jets as a $\mathbb{C}$-ve
Externí odkaz:
http://arxiv.org/abs/2102.03182
Publikováno v:
International Mathematics Research Notices, rnac016, 2022
In this article, we investigate Maximum Likelihood Estimation with tools from Tropical Geometry and Bernstein--Sato theory. We investigate the critical points of very affine varieties and study their asymptotic behavior. We relate these asymptotics t
Externí odkaz:
http://arxiv.org/abs/2101.03570