Related papers: Dimensional reduction and a Z(3) symmetric model
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external…
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce…
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…
Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension…
We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall…
3D reconstruction from a single RGB image is a challenging problem in computer vision. Previous methods are usually solely data-driven, which lead to inaccurate 3D shape recovery and limited generalization capability. In this work, we focus…
We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, Chinese Academy of Sciences, Beijing, 2012] of the author…
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
The first numerical solution of the 3-D travel time tomography problem is presented. The globally convergent convexification numerical method is applied.
In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…
By relating the two-dimensional U(N) Principal Chiral Model to a simple linear system we obtain a free-field parametrisation of solutions. Obvious symmetry transformations on the free-field data give symmetries of the model. In this way all…
In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we used in the reduction of DMSs with nonholonomic constraints,…
The aim of the present paper is to highlight the main results of common work with J. Lukierski and W. Zakrzewski on nonrelativistic particle models on the noncommutative plane and round them off by some new results.
Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower…
An application of dimensional reduction results for gradient constrained problems is provided for 3D-2D dimension reduction for supremal functionals, in the case when the domain is convex.
General formulas for the construction of exact solutions of the equation of the minimal surface in $R^3$, which appears in various physical problems, have been derived by the Zakharov-Shabat "dressing" method. Particular examples are…
A 3-dimensional reduction of the seld-dual Yang-Mills (SDYM) equation, named SDYM3, is examined from the point of view of its symmetry and integrability characteristics. By using a non-auto-Backlund transformation, this equation is…
We analyze a variety of Weyl invariant dynamical problems in three dimensions.
We determine Killing vector fields on the $3$-dimensional space $\mathbb R^3$ endowed with a special diagonal metric.
Given the important role of discrete gauge symmetries in viable models, we discuss these symmetries in intersecting D6-brane trinification model where the ZN symmetry is investigated and its identification is shown.