Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Dey, Papri"'
Autor:
Blekherman, Grigoriy, Dey, Papri
Lorentzian polynomials are a fascinating class of real polynomials with many applications. Their definition is specific to the nonnegative orthant. Following recent work, we examine Lorentzian polynomials on proper convex cones. For a self-dual cone
Externí odkaz:
http://arxiv.org/abs/2405.12973
Autor:
Dey, Papri
We study the class of polynomials whose Hessians evaluated at any point of a closed convex cone have Lorentzian signature. This class is a generalization to the remarkable class of Lorentzian polynomials. We prove that hyperbolic polynomials and coni
Externí odkaz:
http://arxiv.org/abs/2206.02759
Publikováno v:
ITCS 2023
We study the bit complexity of two related fundamental computational problems in linear algebra and control theory. Our results are: (1) An $\tilde{O}(n^{\omega+3}a+n^4a^2+n^\omega\log(1/\epsilon))$ time algorithm for finding an $\epsilon-$approximat
Externí odkaz:
http://arxiv.org/abs/2109.13956
Autor:
Dey, Papri, Edidin, Dan
Let ${\mathcal A} = \{A_{1},\dots,A_{r}\}$ be a collection of linear operators on ${\mathbb R}^m$. The degeneracy locus of ${\mathcal A}$ is defined as the set of points $x \in {\mathbb P}^{m-1}$ for which rank$([A_1 x \ \dots \ A_{r} x]) \\ \leq m-1
Externí odkaz:
http://arxiv.org/abs/2105.14970
Autor:
Dey, Papri, Srinivasan, Hema
Principal matrices of a numerical semigroup of embedding dimension n are special types of $n \times n$ matrices over integers of rank $\leq n - 1$. We show that such matrices and even the pseudo principal matrices of size n must have rank $\geq \frac
Externí odkaz:
http://arxiv.org/abs/2012.15464
Autor:
Chen, Justin, Dey, Papri
Orthostochastic matrices are the entrywise squares of orthogonal matrices, and naturally arise in various contexts, including notably definite symmetric determinantal representations of real polynomials. However, defining equations for the real varie
Externí odkaz:
http://arxiv.org/abs/2001.10691
Given a proper cone $K \subseteq \mathbb{R}^n$, a multivariate polynomial $f \in \mathbb{C}[z] = \mathbb{C}[z_1, \ldots, z_n]$ is called $K$-stable if it does not have a root whose vector of the imaginary parts is contained in the interior of $K$. If
Externí odkaz:
http://arxiv.org/abs/1908.11124
Autor:
Chen, Justin, Dey, Papri
Publikováno v:
J. Softw. Alg. Geom. 10 (2020) 9-15
We introduce the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e. cubics and quartics). Our algorithms a
Externí odkaz:
http://arxiv.org/abs/1905.07035
Autor:
Dey, Papri, Plaumann, Daniel
Hyperbolic polynomials are real multivariate polynomials with only real roots along a fixed pencil of lines. Testing whether a given polynomial is hyperbolic is a difficult task in general. We examine different ways of translating hyperbolicity into
Externí odkaz:
http://arxiv.org/abs/1810.04055
We introduce and study coordinate-wise powers of subvarieties of $\mathbb{P}^n$, i.e. varieties arising from raising all points in a given subvariety of $\mathbb{P}^n$ to the $r$-th power, coordinate by coordinate. This corresponds to studying the im
Externí odkaz:
http://arxiv.org/abs/1807.03295