Estimating Invariant Probability Densities for Dynamical Systems

Knowing a probability density (ideally, an invariant density) for the trajectories of a dynamical system allows many significant estimates to be made, from the well-known dynamical invariants such as Lyapunov exponents and mutual information to conditional probabilities which are potentially more suitable for prediction than the single number produced by most predictors. Densities on typical attractors have properties, such as singularity with respect to Lebesgue measure, which make standard density estimators less useful than one would hope. In this paper we present a new method of estimating densities which can smooth in a way that tends to preserve fractal structure down to some level, and that also maintains invariance. We demonstrate with applications to real and artificial data.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Structure and function of a lignostilbene-α,β-dioxygenase orthologue from <Emphasis Type="Italic">Pseudomonas brassicacearum</Emphasis>

Background

Stilbene cleaving oxygenases (SCOs), also known as lignostilbene-α,β-dioxygenases (LSDs) mediate the oxidative cleavage of the olefinic double bonds of lignin-derived intermediate phenolic stilbenes, yielding small modified benzaldehyde compounds. SCOs represent one branch of the larger carotenoid cleavage oxygenases family. Here, we describe the structural and functional characterization of an SCO-like enzyme from the soil-born, bio-control agent Pseudomonas brassicacearum.

Methods

In vitro and in vivo assays relying on visual inspection, spectrophotometric quantification, as well as liquid-chormatographic and mass spectrometric characterization were applied for functional evaluation of the enzyme. X-ray crystallographic analyses and in silico modeling were applied for structural investigations.

Results

In vitro assays demonstrated preferential cleavage of resveratrol, while in vivo analyses detected putative cleavage of the straight chain carotenoid, lycopene. A high-resolution structure containing the seven-bladed β-propeller fold and conserved 4-His-Fe unit at the catalytic site, was obtained. Comparative structural alignments, as well as in silico modelling and docking, highlight potential molecular factors contributing to both the primary in vitro activity against resveratrol, as well as the putative subsidiary activities against carotenoids in vivo, for future validation.

Conclusions

The findings reported here provide validation of the SCO structure, and highlight enigmatic points with respect to the potential effect of the enzyme’s molecular environment on substrate specificities for future investigation.

     

Hydroxyproline quantification for the estimation of collagen in tissue using multiple reaction monitoring mass spectrometry

Collagens are highly abundant mammalian proteins that contain a high content of hydroxylated amino acids such as hydroxyproline. We have exploited the high hydroxyproline content of collagen and developed a method for hydroxyproline quantification as a measure of collagen content in muscle samples. The novel method utilizes a highly selective and sensitive method of multiple reaction monitoring (MRM) by mass spectrometry. The analytical method is simple, rapid (5min), convenient (no derivatization), precise (<17% RSD), accurate (90-108%), sensitive (4.88nmol/L) and linear (R(2)>0.999) over three orders of magnitude (5-5000nmol/L).     

Permanently oriented antibody immobilization for digoxin determination with a flow-through fluoroimmunosensor

This paper reports a new flow-through fluoroimmunosensor, the function of which is based on antibodies immobilized on an inmunoreactor of controlled-pore glass (CPG), for determination of digoxin, used in the treatment of congestive heart failure and artery disease. The immunosensor has a detection limit of 1.20 microg L(-1) and provides high reproducibility (RSD=4.5% for a concentration of 0.0025 mg L(-1), and RSD=6.7% for 0.01 mg L(-1)). The optimum working concentration range was found to be 1.2 x 10(-3)-4.0 x 10(-2) mg L(-1). The lifetime of the immunosensor was about 50 immunoassays; if stored unused its lifetime can be extended to three months. A sample speed of about 10-12 samples per hour can be attained. Possible interference from substances with structures similar to digoxin (morphine, heroin, tebaine, codeine, pentazocine and narcotine) was investigated. No cross-reactivity was seen at the highest digoxin: interferent ratio studied (1:100). The proposed fluoroimmunosensor was successfully used to determine digoxin concentrations in human serum samples.     

Parameter inference in small world network disease models with approximate Bayesian Computational methods

Small world network models have been effective in capturing the variable behaviour of reported case data of the SARS coronavirus outbreak in Hong Kong during 2003. Simulations of these models have previously been realized using informed “guesses” of the proposed model parameters and tested for consistency with the reported data by surrogate analysis. In this paper we attempt to provide statistically rigorous parameter distributions using Approximate Bayesian Computation sampling methods. We find that such sampling schemes are a useful framework for fitting parameters of stochastic small world network models where simulation of the system is straightforward but expressing a likelihood is cumbersome.