A new entropy measure based on the Renyi entropy rate using Gaussian kernels

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

Amplitude response of a unilaterally constrained nonlinear micromechanical resonator

Dynamical systems that involve impacts frequently arise in engineering. This Letter reports a study of such a system at microscale that consists of a nonlinear resonator operating with an unilateral impact. The microresonators were fabricated on silicon-on-insulator wafers by using a one-mask process and then characterised by using the capacitively driving and sensing method. Numerical results concerning the dynamics of this vibro-impact system were verified by the experiments. Bifurcation analysis was used to provide a qualitative scenario of the system steady-state solutions as a function of both the amplitude and the frequency of the external driving sinusoidal voltage. The results show that the amplitude of resonant peak is levelled off owing to the impact effect and that the bandwidth of impacting is dependent upon the nonlinearity and the operating conditions.

Bayesian online algorithms for learning in discrete Hidden Markov Models

We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.

LacO-LacI interaction in affinity adsorption of plasmid DNA

Current approaches for purifying plasmids from bacterial production systems exploit the physiochemical properties of nucleic acids in non-specific capture systems. In this study, an affinity system for plasmid DNA (pDNA) purification has been developed utilizing the interaction between the lac operon (lacO) sequence contained in the pDNA and a 64mer synthetic peptide representing the DNA-binding domain of the lac repressor protein, LacI. Two plasmids were evaluated, the native pUC19 and pUC19 with dual lacO3/lacOs operators (pUC19lacO3/lacOs), where the lacOs operator is perfectly symmetrical. The DNA-protein affinity interaction was evaluated by surface plasmon resonance using a Biacore system. The affinity capture of DNA in a chromatography system was evaluated using LacI peptide that had been immobilized to Streamline™ adsorbent. The KD-values for double stranded DNA (dsDNA) fragments containing lacO1 and lacO3 and lacOs and lacO3 were 5.7 ± 0.3 × 10 -11 M and 4.1 ± 0.2 × 10-11 M respectively, which compare favorably with literature reports of 5 × 10-10 - 1 × 10-9 M for native laCO1 and 1-1.2 × 10-10 M for lacO1 in a saline buffer. Densitometric analysis of the gel bands from the affinity chromatography run clearly showed a significant preference for capture of the supercoiled fraction from the feed pDNA sample. The results indicate the feasibility of the affinity approach for pDNA capture and purification using native protein-DNA interaction. © 2006 Wiley Periodicals, Inc.

A pragmatic Bayesian approach to wind field retrieval

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

Knowledge-based Robot Control

The paper is related with the problem of developing autonomous intelligent robots for complex environments. In details it outlines a knowledge-based robot control architecture that combines several techniques in order to supply an ability to adapt and act autonomously in complex environments. The described architecture has been implemented as a robotic system that demonstrates its operation in dynamic environment. Although the robotic system demonstrates a certain level of autonomy, the experiments show that there are situation, in which the developed base architecture should be complemented with additional modules. The last few chapters of the paper describe the experimentation results and the current state of further research towards the developed architecture.

Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations

Oscillation criteria are given for the second order sublinear non-autonomous differential equation. (r(t) (x)x′(t))′ + q(t)g(x(t)) = (t). These criteria extends and improves earlier oscillation criteria of Kamenev, Kura, Philos and Wong. Oscillation criteria are also given for second order sublinear damped non-autonomous differential equations.