Dimensional and Scaling Analysis

Dimensional analysis and scaling laws

Upscaling river biomass using dimensional analysis and hydrogeomorphic scaling

[1] We propose a methodology for upscaling biomass in a river using a combination of dimensional analysis and hydro-geomorphologic scaling laws. We first demonstrate the use of dimensional analysis for determining local scaling relationships between Nostoc biomass and hydrologic and geomorphic variables. We then combine these relationships with hydraulic geometry and streamflow scaling in order...

Scaling Laws from Statistical Data and Dimensional Analysis

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad-hoc, tedious, and time consuming. Here we present an algorithm that obtains a scaling law in the form of a power law from experimental data...

Incremental Multi-Dimensional Scaling

Multi-Dimensional Scaling (MDS) is a widely used method for embedding a given distance matrix into a low dimensional space, used both as a preprocessing step for many machine learning problems, as well as a visualization tool in its own right. In this paper, we present an incremental version of MDS (iMDS). In iMDS, d-dimensional data points are presented in a stream, and the task is to embed th...

Discrete Multi-Dimensional Scaling

In recent years, a number of models of lexical access based on attractor networks have appeared. These models reproduce a number of effects seen in psycholinguistic experiments, but all suffer from unrealistic representations of lexical semantics. In an effort to improve this situation we are looking at techniques developed in the information retrieval literature that use the statistics found i...