We investigate the laws that rule the behavior of the largest Lyapunov exponent (LLE) in many particle systems with long-range interactions. We consider as a representative system the so-called Hamiltonian alpha-XY model where the adjustable parameter alpha controls the range of the interactions of N ferromagnetic spins in a lattice of dimension d. In previous work the dependence of the LLE wit...

We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian Markov random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting model, which we call maximum entropy unfolding (MEU) is a nonlinear generalization of principal component analysis. We relat...

In this paper, vector field learning is proposed as a new application of manifold learning to vector field. We also provide a learning framework to extract significant features from vector data. Vector data containing position, direction and magnitude information is different from common point data only containing position information. The algorithm of locally linear embedding (LLE) is extended...

We present a Python toolkit for simulating the propagation dynamics of dissipative solitons in variant Lugiato–Lefever equation (LLE) including dispersion terms third and fourth order. In addition, provided software allows to prepare initial conditions given by stationary localized solutions standard LLE anomalous group-velocity regime. Propagation scenarios custom control parameters can be spe...

In the field of bioanalysis, there is an increasing demand for miniaturized, automated, robust sample pretreatment procedures that can be easily connected to direct-infusion mass spectrometry (DI-MS) in order to allow the high-throughput screening of drugs and/or their metabolites in complex body fluids like plasma. Liquid-Liquid extraction (LLE) is a common sample pretreatment technique often ...

Gaussian fields (GF) have recently received considerable attention for dimension reduction and semi-supervised classification. In this paper we show how the GF framework can be used for semi-supervised regression on high-dimensional data. We propose an active learning strategy based on entropy minimization and a maximum likelihood model selection method. Furthermore, we show how a recent genera...

Dimensionality reduction is the search for a small set of variables to describe a large set of observed dimensions. Some benefits of dimensionality reduction include data visualization, compact representation, and decreased processing time. In this paper, we review two nonlinear techniques for dimensionality reduction: Isometric Feature Mapping (Isomap) and Locally Linear Embedding (LLE), and a...

There has been a renewed interest in understanding thestructure of high dimensional data set based on manifoldlearning. Examples include ISOMAP [25], LLE [20]and Laplacian Eigenmap [2] algorithms. Most of thesealgorithms operate in a “batch” mode and cannot beapplied efficiently for a data stream. We propose anincremental version of ISOMAP. Our experiments notonly de...

We studied a relation of chaotic dynamics of finger plethysmogram to complexity of high cerebral center in both theoretical and experimental approaches. We proposed a mathematical model to describe emergence of chaos in finger tip pulse wave, which gave a theoretical prediction indicating increased chaoticity in higher cerebral center leading to an increase of chaos dynamics in plethysmograms. ...

This paper presents a novel cross-layer approach (LLE-TCP) designed for performance enhancement of TCP over a large variety of wireless networks. LLE-TCP avoids TCP ACK packet transmission over the wireless channel. As a result, the saved time can be utilized by the nodes for data packet delivery. The proposed scheme enhances the protocol stacks of the wireless sender (or a base station) and th...