Zobrazeno 1 - 10
of 125
pro vyhledávání: '"Pavlov, Dmitrii A."'
In these notes we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are o
Externí odkaz:
http://arxiv.org/abs/2410.11757
The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide a combina
Externí odkaz:
http://arxiv.org/abs/2409.04288
Autor:
Pavlov, Dmitrii, Telen, Simon
The Santal\'o point of a convex polytope is the interior point which leads to a polar dual of minimal volume. This minimization problem is relevant in interior point methods for convex optimization, where the logarithm of the dual volume is known as
Externí odkaz:
http://arxiv.org/abs/2402.18955
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical models are fami
Externí odkaz:
http://arxiv.org/abs/2308.11538
A Grasstope is the image of the totally nonnegative Grassmannian $\text{Gr}_{\geq 0}(k,n)$ under a linear map $\text{Gr}(k,n)\dashrightarrow \text{Gr}(k,k+m)$. This is a generalization of the amplituhedron, a geometric object of great importance to c
Externí odkaz:
http://arxiv.org/abs/2307.09603
Given a single algebraic input-output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand sides. It has been shown tha
Externí odkaz:
http://arxiv.org/abs/2303.16799
Autor:
Pavlov, Dmitrii
A positive definite matrix is called logarithmically sparse if its matrix logarithm has many zero entries. Such matrices play a significant role in high-dimensional statistics and semidefinite optimization. In this paper, logarithmically sparse matri
Externí odkaz:
http://arxiv.org/abs/2301.10042
Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum~physics, where they extend the ubiquitous role of toric geometry. The Gibbs variety i
Externí odkaz:
http://arxiv.org/abs/2211.15490
Autor:
Pavlov, Dmitrii, Pogudin, Gleb
Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs of the sys
Externí odkaz:
http://arxiv.org/abs/2203.03555
Ritt's theorem of zeroes and Seidenberg's embedding theorem are classical results in differential algebra allowing to connect algebraic and model-theoretic results on nonlinear PDEs to the realm of analysis. However, the existing proofs of these resu
Externí odkaz:
http://arxiv.org/abs/2107.03012