Parametric scaling of mathematical models

Mathematical approaches to dynamic scaling

Studies of phase separation lead to many interesting probems in non-equilibrium thermodynamics. The hypothesis of ynamic scaling plays an essential role in our understandng of such processes (see for example, Ref. [1]). This is a ell-tested hypothesis based on experiments and determinisic and stochastic numerical simulations. This article is a short ntroduction to mathematical methods useful in...

Parametric Models

Simulation of Pedestrian Dynamics with Macroscopic and Microscopic Mathematical Models

Here, we collect two parts of a research project on the pedestrian flow modeling. Rapid growth in the volume of public transport and the need for its reasonable, efficient planning have made the description and modeling of transport and pedestrian behaviors as important research topics in the past twenty years. First, we present a macroscopic model for the pedestrian flow based on continuum mec...

Multidimensional Scaling Visualization Using Parametric Similarity Indices

Abstract: In this paper, we apply multidimensional scaling (MDS) and parametric similarity indices (PSI) in the analysis of complex systems (CS). Each CS is viewed as a dynamical system, exhibiting an output time-series to be interpreted as a manifestation of its behavior. We start by adopting a sliding window to sample the original data into several consecutive time periods. Second, we define ...

Parametric Manifold Learning Via Sparse Multidimensional Scaling

We propose a metric-learning framework for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We employ Siamese networks to solve the problem of least squares multidimensional scaling for generating mappings that preserve geodesic distances on the manifold. In contrast to previous parametric manifold learning methods we show a substanti...