Stochastic gradient descent remains popular in large-scale machine learning, on account of its very low computational cost and robustness to noise. However, gradient descent is only linearly efficient and not transformation invariant. Scaling by a local measure can substantially improve its performance. One natural choice of such a scale is the Hessian of the objective function: Were it availab...

This thesis deals with the solution of a nonlinear inverse problem arising in digital image registration. In image registration one seeks to compute a transformation between two images such that they become more similar in some sense. In the first part, we define the problem as the minimization of a regularized nonlinear least-squares functional, which measures the image difference and smoothne...

The notion of Newton polygon is well-known. We deene a generali-sation and apply it to study polar curves, Lojasiewicz exponents, singularities at innnity of complex polynomials (Ha Huy Vui's theorem), and-constant deformations. Philosophically speaking, the Newton polygon relative to an arc exposes f in a horn neighborhood of. The gradient of a function behaves erratically in the process of bl...

The technology of three-dimensional reconstruction based on visual sensor has become an important research aspect. Based on Newton iteration algorithm, the improved 3D normal distribution transformation algorithm” (NI-3DNDT) is put forward, aiming to fix the problem of discrete point cloud registration algorithm in poor astringency and being open to local optimum. The discrete 3d point cloud ad...

Given a Laurent polynomial f , one can form the period of f : this is a function of one complex variable that plays an important role in mirror symmetry for Fano manifolds. Mutations are a particular class of birational transformations acting on Laurent polynomials in two variables; they preserve the period and are closely connected with cluster algebras. We propose a higher-dimensional analog ...

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational “dynamical exponent”, z. The Schrödinger-Virasoro algebra of Henkel et ...

It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton’s laws. On the other hand, literature analyzes the way in which forces transform under a change of reference frame. Notwithstanding, no analogous study is done for the way in which work and energy transform under those changes of reference frames. We analyze the behavior of energy and work unde...

We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Newton relations and Cayley-Hamilton theorem for the matrix of generators of the RE algebra related to a finite rank even Hecke symmetry are derived.

We construct a class of transformations similar to the Pascal transformation, except for the use of spacers, and show that these transformations are weakly mixing.