Hybrid deterministic/stochastic algorithm for large sets of rate equations

We propose a hybrid algorithm for the time integration of large sets of rate equations coupled by a relatively small number of degrees of freedom. A subset containing fast degrees of freedom evolves deterministically, while the rest of the variables evolves stochastically. The emphasis is put on the coupling between the two subsets, in order to achieve both accuracy and efficiency. The algorithm is tested on the problem of nucleation, growth and coarsening of clusters of defects in iron, treated by the formalism of cluster dynamics. We show that it is possible to obtain results indistinguishable from fully deterministic and fully stochastic calculations, while speeding up significantly the computations with respect to these two cases.Comment: 9 pages, 7 figure

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Determination of Soybean Oil, Protein and Amino Acid Residues in Soybean Seeds by High Resolution Nuclear Magnetic Resonance (NMRS) and Near Infrared (NIRS)

A detailed account is presented of our high resolution nuclear magnetic resonance (HR-NMR) and near infrared (NIR) calibration models, methodologies and validation procedures, together with a large number of composition analyses for soybean seeds. NIR calibrations were developed based on both HR-NMR and analytical chemistry reference data for oil and twelve amino acid residues in mature soybeans and soybean embryos. This is our first report of HR-NMR determinations of amino acid profiles of proteins from whole soybean seeds, without protein extraction from the seed. It was found that the best results for both oil and protein calibrations were obtained with a Partial Least Squares Regression (PLS-1) analysis of our extensive NIR spectral data, acquired with either a DA7000 Dual Diode Array (Si and InGaAs detectors) instrument or with several Fourier Transform NIR (FT-NIR) spectrometers equipped with an integrating sphere/InGaAs detector accessory. In order to extend the bulk soybean samples calibration models to the analysis of single soybean seeds, we have analized in detail the component NIR spectra of all major soybean constituents through spectral deconvolutions for bulk, single and powdered soybean seeds. Baseline variations and light scattering effects in the NIR spectra were corrected, respectively, by calculating the first-order derivatives of the spectra and the Multiplicative Scattering Correction (MSC). The single soybean seed NIR spectra are broadly similar to those of bulk whole soybeans, with the exception of minor peaks in single soybean NIR spectra in the region from 950 to 1,000 nm. Based on previous experience with bulk soybean NIR calibrations, the PLS-1 calibration model was selected for protein, oil and moisture calibrations that we developed for single soybean seed analysis. In order to improve the reliability and robustness of our calibrations with the PLS-1 model we employed standard samples with a wide range of soybean constituent compositions: from 34% to 55% for protein, from 11% to 22% for oil and from 2% to 16% for moisture. Such calibrations are characterized by low standard errors and high degrees of correlation for all major soybean constituents. Morever, we obtained highly resolved NIR chemical images for selected regions of mature soybean embryos that allow for the quantitation of oil and protein components. Recent developments in high-resolution FT-NIR microspectroscopy extend the NIR sensitivity range to the picogram level, with submicron spatial resolution in the component distribution throughout intact soybean seeds and embryos. Such developments are potentially important for biotechnology applications that require rapid and ultra- sensitive analyses, such as those concerned with high-content microarrays in Genomics and Proteomics research. Other important applications of FT-NIR microspectroscopy are envisaged in biomedical research aimed at cancer prevention, the early detection of tumors by NIR-fluorescence, and identification of single cancer cells, or single virus particles in vivo by super-resolution microscopy/ microspectroscopy

Prospects and Limitations of Algorithmic Cooling

Heat-bath algorithmic cooling (AC) of spins is a theoretically powerful effective cooling approach, that (ideally) cools spins with low polarization exponentially better than cooling by reversible entropy manipulations alone. Here, we investigate the limitations and prospects of AC. For non-ideal and semioptimal AC, we study the impact of finite relaxation times of reset and computation spins on the achievable effective cooling. We derive, via simulations, the attainable cooling levels for given ratios of relaxation times using two semioptimal practicable algorithms. We expect this analysis to be valuable for the planning of future experiments. For ideal and optimal AC, we make use of lower bounds on the number of required reset steps, based on entropy considerations, to present important consequences of using AC as a tool for improving signal-to-noise ratio in liquid-state magnetic resonance spectroscopy. We discuss the potential use of AC for noninvasive clinical diagnosis and drug monitoring, where it may have significantly lower specific absorption rate (SAR) with respect to currently used methods.Comment: 12 pages, 5 figure