To enable the user to visualize their own brain activity is an essential part of a Brain-Computer Interface (BCI). For visualization, we need a dimension reduction algorithm, because only a few relevant components of the high-dimensional feature vectors, extracted from the electroencephalogram (EEG) signals, can be visualized. For this purpose, three feature mapping methods, Principal Component...

We show that the thermodynamic entropy density is proportional to the largest Lyapunov exponent (LLE) of a discrete hydrodynamical system, a deterministic two-dimensional lattice gas automaton. The definition of the LLE for cellular automata is based on the concept of Boolean derivatives and is formally equivalent to that of continuous dynamical systems. This relation is justified using a Marko...

Low-loss electron (LLE) imaging in the scanning electron microscope (SEM) is based on the collection of backscattered electrons that have undergone minimal elastic interactions within a sample and therefore carry high-resolution, surface-specific information. Oliver Wells credits the concept of filtering the high-energy emitted electrons in the SEM to a statement made by McMullan [2], that the ...

Within a quantum molecular dynamics model we calculate the largest Lyapunov exponent (LLE), density fluctuation and mass distribution of fragments for a series of nuclear systems at different initial temperatures. It is found that the LLE peaks at the temperature (”critical temperature”) where the density fluctuation reaches a maximal value and the mass distribution of fragments is best fitted ...

This paper presents a novel method to recognize high density crowd behaviors using micro-behaviors combining with Sparse Representation based on Locally Linear Embedding (named LLE-based Sparse Representation or LLE-SR). We extract micro-behaviors from each frame, respectively named Fountainhead, Bottleneck, Blocking, Lane and Ring/Arch, and construct micro-behaviors histograms to better descri...

Recently, a new method intended to realize conformal mappings has been published. Called Locally Linear Embedding (LLE), this method can map high-dimensional data lying on a manifold to a representation of lower dimensionality that preserves the angles. Although LLE is claimed to solve problems that are usually managed by neural networks like Kohonen’s Self-Organizing Maps (SOMs), the method re...

We study the linear dynamics of spectrally stable T -periodic stationary solutions Lugiato-Lefever equation (LLE), a damped nonlinear Schrödinger with forcing that arises in optics. Such are nonlinearly to NT -periodic, i.e. subharmonic, perturbations for each N ∈ exponential decay rates form e − δ t . However, both and allowable size initial tend 0 as → ∞ , so this result is non-uniform and, f...

The liquid-liquid equilibrium (LLE) phase boundaries were determined experimentally for the ternary systems containing refined sunflower oil, methanol, and one of ten potential cosolvents at 308.2 K under atmospheric pressure by using cloud point method. n-Butylamine was found to be one of the best cosolvents, which could substantially enhance the miscibility between the oil and methanol. The L...

Subspace manifold learning represents a popular class of techniques in statistical image analysis and object recognition. Recent research in the field has focused on nonlinear representations; locally linear embedding (LLE) is one such technique that has recently gained popularity. We present and apply a generalization of LLE that introduces sample weights. We demonstrate the application of the...

A new pH-sensing film was developed by using tamarind seed polysaccharide (TSP) and natural dye extracted from litmus lichen (LLE). The addition of LLE from 0 to 2.5% decreased the tensile strength and elongation at break from 30.20 to 29.97 MPa and 69.73% to 60.13%, respectively, but increased the water vapor permeability from 0.399 × 10−9 to 0.434 × 10−9 g·s−1·m−1·Pa−1. The UV–Vis spectra of ...