Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Rose, Kemal"'
Autor:
Rose, Kemal, Telek, Máté L.
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute the positive tropicalization, offering a real analogue to the Fundamen
Externí odkaz:
http://arxiv.org/abs/2408.15719
Autor:
Rose, Kemal
Systems of polynomial equations appear both in mathematics, as well as in many applications in the sciences, economics and engineering. Solving these systems is at the heart of computational algebraic geometry, a field which is often associated with
Externí odkaz:
https://ul.qucosa.de/id/qucosa%3A92869
https://ul.qucosa.de/api/qucosa%3A92869/attachment/ATT-0/
https://ul.qucosa.de/api/qucosa%3A92869/attachment/ATT-0/
Autor:
Hilany, Boulos El, Rose, Kemal
Two continuous maps $f, g : \mathbb{C}^2\to\mathbb{C}^2$ are said to be topologically equivalent if there exist homeomorphisms $\varphi,\psi:\mathbb{C}^2\to\mathbb{C}^2$ satisfying $\psi\circ f\circ\varphi = g$. It is known that there are finitely ma
Externí odkaz:
http://arxiv.org/abs/2402.08993
We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of critical points to these problems, one as a mixed volume and one as an inte
Externí odkaz:
http://arxiv.org/abs/2308.07765
Tropical implicitization means computing the tropicalization of a unirational variety from its parametrization. In the case of a hypersurface, this amounts to finding the Newton polytope of the implicit equation, without computing its coefficients. W
Externí odkaz:
http://arxiv.org/abs/2306.13015
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that explicitly c
Externí odkaz:
http://arxiv.org/abs/2302.04117
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation, the proble
Externí odkaz:
http://arxiv.org/abs/2211.09439
Autor:
Rose, Kemal
We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the generic n
Externí odkaz:
http://arxiv.org/abs/2209.10670
Autor:
Rose, Kemal
We describe the non-Gorenstein loci of normal toric varieties. In the case of Hibi rings a combinatorial description is provided in terms of the underlying partially ordered set. As a non-toric application we compute the dimensions of the non-Gorenst
Externí odkaz:
http://arxiv.org/abs/2204.01317
We study lines on smooth cubic surfaces over the field of $p$-adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines are $0,1,2,3,5,7,9,15$ or $27$. We show that each of these counts is a
Externí odkaz:
http://arxiv.org/abs/2202.03489