Related papers: On variational dimension reduction in structure me…
The relationship according to which one physical theory encompasses the domain of empirical validity of another is widely known as "reduction." Here it is argued that one popular methodology for showing that one theory reduces to another,…
Dimensional deconstruction (DD) abstracts from higher dimensional models features of related 4--dimensional ones. DD was proposed in Refs.[1,2,3] as a scheme for constructing models of {\it naturally} light composite Higgs boson. These are…
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…
Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly…
In this paper, we derive the first variation formulas for surfaces in 3-dimensional Euclidean space by using the ``strain-displacement relations'' known in thin shell theory. For applications to architectural surface design, we focus on the…
It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…
Standard spring design is based on the assumption that there is no residual stress in the wire. This assumption can be quite strong for small wires that undergo a significant wire drawing during the manufacturing process. The main objective…
This work aims to provide standard formulations for direct minimization approaches on various types of static problems of continuum mechanics. Particularly, form-finding problems of tension structures are discussed in the first half and the…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
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…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
Minimal surfaces are among the most natural objects in Differential Geometry, and have been studied for the past 250 years ever since the pioneering work of Lagrange. The subject is characterized by a profound beauty, but perhaps even more…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model…
In the usual procedure for toroidal Kaluza-Klein reduction, all the higher-dimensional fields are taken to be independent of the coordinates on the internal space. It has recently been observed that a generalisation of this procedure is…
In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces, reducing the system to a collection of (D-n)-dimensional fields. This allows one…
Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from…
Since its first use by Behrend, Bryan, and Szendr\H{o}i in the computation of motivic Donaldson-Thomas (DT) invariants of $\mathbb{A}_{\mathbb{C}}^3$, dimensional reduction has proved to be an important tool in motivic and cohomological DT…