Related papers: On variational dimension reduction in structure me…
Dimension reduction is often needed in the area of data mining. The goal of these methods is to map the given high-dimensional data into a low-dimensional space preserving certain properties of the initial data. There are two kinds of…
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…
We investigate the connection between a formal property of the critical behavior of several systems in the presence of quenched disorder, known as "dimensional reduction", and the presence in the same systems at zero temperature of…
Ptychographic reconstructions in reflection geometries are commonly interpreted with the same two-dimensional thin-sample model used in transmission, yet the validity of this approximation has not been established. We develop a…
In aircraft industry, market needs evolve quickly in a high competitiveness context. This requires adapting a given aircraft model in minimum time considering for example an increase of range or the number of passengers (cf A330 NEO…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
This paper aims to study the convergence of solutions in three-dimensional nonlinear elastodynamics for a thin rod as its cross section shrinks to zero for displacements that are comparable to the small radius of the rod. Assuming the…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…
This work addresses models (e.g. potential models of directed orbital systems- the manganates) in which an effective reduction dimensionality occurs as a result of a new symmetry which is intermediate between that of global and local gauge…
We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
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…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
Many techniques in machine learning attempt explicitly or implicitly to infer a low-dimensional manifold structure of an underlying physical phenomenon from measurements without an explicit model of the phenomenon or the measurement…
We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…
We present, in a pedagogical style, many instances of reduction procedures appearing in a variety of physical situations, both classical and quantum. We concentrate on the essential aspects of any reduction procedure, both in the algebraic…
In the direct approach to continua in reduced space dimensions, a thin shell is described as a mathematical surface in three-dimensional space. An exploratory kinematic study of such surfaces could be very valuable, especially if conducted…
The physical motivations and the basic construction rules for Type I strings and M-theory compactifications are reviewed in light of the recent developments. The first part contains the basic theoretical ingredients needed for building…